View Full Version : The Superstring "Landscape"
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Hello dear group.\n\nAs well known, one the current problems of superstring theory\nis the supposed existence of huge number of possible vacua,\ni.e. superselection sectors, without any natural selection\nmechanism. Estimates such as 10^100 have been proposed for\nthis number. To cure the illness, the anthropic principle has\nbeen called forward which issued a great deal of argument in\nthe community.\n\nBefore I failed to realize how come we get a finite number of\nsectors rather than a mutli-dimension space of them. After\nall we may compactify string theory on a 6D manifold with a\nmulti-dimensional moduli space + add fluxes and D-branes to\nour heart content (modulo some anomaly cancellation\nconditions, methinks). Not mentioning using a negative\ncosmological constant in addition.\n\nThen, someone tried to convince me a quantum potential is\ndynamically generated on the moduli space, therefore, only\nits minima remain as valid vacua.\n\n1) How can this quantum potential be computer or merely\ndefined, at least in principle?\n\n2) It is the global minima only which should correspond to\ntrue vacua. The rest should give us metastable states.\nHowever, how in the hell can we get around 10^100 global\nminima?! Moreover, this minima can\'t be related by\nsymmetries since such minima display equivalent physics. If\nso, numbers such as 10^100 appear utterly unlikely.\n\n3) Do I understand correctly there is supposed to be a\nmechanism which quantizes the cosmological constant? Even\nlimits it to a finite set of values, possibly? What is this\nmechanism?\n\nBest regards,\nSquark.\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Hello dear group.
As well known, one the current problems of superstring theory
is the supposed existence of huge number of possible vacua,
i.e. superselection sectors, without any natural selection
mechanism. Estimates such as 10^100 have been proposed for
this number. To cure the illness, the anthropic principle has
been called forward which issued a great deal of argument in
the community.
Before I failed to realize how come we get a finite number of
sectors rather than a mutli-dimension space of them. After
all we may compactify string theory on a 6D manifold with a
multi-dimensional moduli space + add fluxes and D-branes to
our heart content (modulo some anomaly cancellation
conditions, methinks). Not mentioning using a negative
cosmological constant in addition.
Then, someone tried to convince me a quantum potential is
dynamically generated on the moduli space, therefore, only
its minima remain as valid vacua.
1) How can this quantum potential be computer or merely
defined, at least in principle?
2) It is the global minima only which should correspond to
true vacua. The rest should give us metastable states.
However, how in the hell can we get around 10^100 global
minima?! Moreover, this minima can't be related by
symmetries since such minima display equivalent physics. If
so, numbers such as 10^100 appear utterly unlikely.
3) Do I understand correctly there is supposed to be a
mechanism which quantizes the cosmological constant? Even
limits it to a finite set of values, possibly? What is this
mechanism?
Best regards,
Squark.
Jake Mannix
May17-04, 05:17 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Squark <fiis5d@yahoo.com> wrote :\n\n> Hello dear group.\n\nHi Squark!\n\n> Then, someone tried to convince me a quantum potential is\n> dynamically generated on the moduli space, therefore, only\n> its minima remain as valid vacua.\n\nI\'m no expert, but at least on this I think I can give you a little\nbit - if you\'re cool with the fact that the manifold M we\ncompactify on has moduli (some related to things like its\noverall size or shape, and others related more to its\nanalytic structure), then once you put fluxes on M, the energy\nof the configuration should depend on moduli around which\nthe fluxes are wrapped.\n\nDid that make sense? If you have higher-form B-field with\nsome integral winding number around some cycle, and\nthere\'s a modulus of M which corresponds to growing or\nshrinking (the size of) that cycle, then it seems plausible\nthat the total energy would no longer be independent of\nthat modulus: i.e. it\'s no long a modulus - there\'s a value\nwhich minimizes the potential.\n\nI\'m told that it\'s expected that with generic (allowed) fluxes,\nall the moduli (well, of either Kahler or Complex type - I\'m\nnot sure how people go about lifting the other once you\'ve\ngot one set under control - I hear mumblings about\n"nonperturbative worldsheet thingamajigs" occasionally\non this) get lifted to a discrete set of allowed possibilities.\n\n> 1) How can this quantum potential be computer or merely\n> defined, at least in principle?\n\nSo in particular choices of CY manifold to compactify on,\nyou know what the moduli are, and as I parenthetically\nalluded to above, you sometimes have a good handle on\n"half" of the moduli, and can yes, see whether the moduli\nare lifted (and can then estimate, based on order of the\nequations defining the minima, the number of distinct\nvacua there are). I\'m still not sure how people go about\npicking what compactification to choose (well, more\nprecisely, I don\'t know that I\'ve heard much in the way\nof how we think *nature* picks which compactification...).\n\n\n> 2) It is the global minima only which should correspond to\n> true vacua. The rest should give us metastable states.\n> However, how in the hell can we get around 10^100 global\n> minima?! Moreover, this minima can\'t be related by\n> symmetries since such minima display equivalent physics. If\n> so, numbers such as 10^100 appear utterly unlikely.\n\nIt\'s not global minima they\'re talking about here: I think it\'s\npretty well assumed that there are indeed globally\nnonperturbatively stable SUSY vacua (11D Minkowski space,\nfor example), which would be global minima of the theory.\n\nThe 10^100 number is counting metastable vacua: SUSY\nis broken in our world, so if the M-theory is the TOE, then\nwe\'re most likely in a metastable (but rather long lived)\n"vacuum". The hugeness of this number comes from the\nfact that CY manifolds often have fairly high dimensional\nmoduli spaces (100+ dimensional isn\'t that rare - the\nquintic, for example, has h^2,1 = 101 alone, iirc), and\nif you put even a fairly simple potential (say, a degree N\npolynomial) on it, a degree N polynomial in *one\nhundred variables* will generically have on the order of\nN^100 minima. This is where people start getting these\nnumbers from (I think - correct me if I\'m wrong, dear\nmoderators!).\n\n> 3) Do I understand correctly there is supposed to be a\n> mechanism which quantizes the cosmological constant? Even\n> limits it to a finite set of values, possibly? What is this\n> mechanism?\n\nYou got me on this one - I don\'t understand any of the\nways people deal with the CC. I haven\'t heard one good\nexplanation of what happens in universes with *any*\npositive value, but maybe I\'m just not as credulous as\nI used to be when I was younger. ;)\n\n-Jake Mannix\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Squark <fiis5d@yahoo.com> wrote :
> Hello dear group.
Hi Squark!
> Then, someone tried to convince me a quantum potential is
> dynamically generated on the moduli space, therefore, only
> its minima remain as valid vacua.
I'm no expert, but at least on this I think I can give you a little
bit - if you're cool with the fact that the manifold M we
compactify on has moduli (some related to things like its
overall size or shape, and others related more to its
analytic structure), then once you put fluxes on M, the energy
of the configuration should depend on moduli around which
the fluxes are wrapped.
Did that make sense? If you have higher-form B-field with
some integral winding number around some cycle, and
there's a modulus of M which corresponds to growing or
shrinking (the size of) that cycle, then it seems plausible
that the total energy would no longer be independent of
that modulus: i.e. it's no long a modulus - there's a value
which minimizes the potential.
I'm told that it's expected that with generic (allowed) fluxes,
all the moduli (well, of either Kahler or Complex type - I'm
not sure how people go about lifting the other once you've
got one set under control - I hear mumblings about
"nonperturbative worldsheet thingamajigs" occasionally
on this) get lifted to a discrete set of allowed possibilities.
> 1) How can this quantum potential be computer or merely
> defined, at least in principle?
So in particular choices of CY manifold to compactify on,
you know what the moduli are, and as I parenthetically
alluded to above, you sometimes have a good handle on
"half" of the moduli, and can yes, see whether the moduli
are lifted (and can then estimate, based on order of the
equations defining the minima, the number of distinct
vacua there are). I'm still not sure how people go about
picking what compactification to choose (well, more
precisely, I don't know that I've heard much in the way
of how we think *nature* picks which compactification...).
> 2) It is the global minima only which should correspond to
> true vacua. The rest should give us metastable states.
> However, how in the hell can we get around 10^100 global
> minima?! Moreover, this minima can't be related by
> symmetries since such minima display equivalent physics. If
> so, numbers such as 10^100 appear utterly unlikely.
It's not global minima they're talking about here: I think it's
pretty well assumed that there are indeed globally
nonperturbatively stable SUSY vacua (11D Minkowski space,
for example), which would be global minima of the theory.
The 10^100 number is counting metastable vacua: SUSY
is broken in our world, so if the M-theory is the TOE, then
we're most likely in a metastable (but rather long lived)
"vacuum". The hugeness of this number comes from the
fact that CY manifolds often have fairly high dimensional
moduli spaces (100+ dimensional isn't that rare - the
quintic, for example, has h^2,1 = 101 alone, iirc), and
if you put even a fairly simple potential (say, a degree N
polynomial) on it, a degree N polynomial in *one
hundred variables* will generically have on the order of
N^{100} minima. This is where people start getting these
numbers from (I think - correct me if I'm wrong, dear
moderators!).
> 3) Do I understand correctly there is supposed to be a
> mechanism which quantizes the cosmological constant? Even
> limits it to a finite set of values, possibly? What is this
> mechanism?
You got me on this one - I don't understand any of the
ways people deal with the CC. I haven't heard one good
explanation of what happens in universes with *any*
positive value, but maybe I'm just not as credulous as
I used to be when I was younger. ;)
-Jake Mannix
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Jake Mannix <jake@rset.net> wrote in message news:<12c1bbee.0405162054.3c204a65-100000@posting.google.com>...\n> I\'m no expert, but at least on this I think I can give you a little\n> bit - if you\'re cool with the fact that the manifold M we\n> compactify on has moduli (some related to things like its\n> overall size or shape, and others related more to its\n> analytic structure)\n\nThis is quite obvious, one can even express the local\ndimension of the moduli space through the cohomology\ndimensions of the CY.\n\n> then once you put fluxes on M, the energy\n> of the configuration should depend on moduli around which\n> the fluxes are wrapped.\n\nThis is probably true, however, it seems unlikely that\nalone would lead to a discrete set of (even local) minima.\nTaking only that into account, one can always obtain an\ninfinity of equal-energy choices by rescaling the flux _and_\nthe moduli.\n\n> > 1) How can this quantum potential be computer or merely\n> > defined, at least in principle?\n>\n> So in particular choices of CY manifold to compactify on,\n> you know what the moduli are, and as I parenthetically\n> alluded to above, you sometimes have a good handle on\n> "half" of the moduli, and can yes, see whether the moduli\n> are lifted (and can then estimate, based on order of the\n> equations defining the minima, the number of distinct\n> vacua there are).\n\nI still don\'t see how you actually compute the quantum\npotential, except computing it for the effective QFT\napproximation of theory. Well, I guess that\'s what they do...\n\n> I\'m still not sure how people go about\n> picking what compactification to choose (well, more\n> precisely, I don\'t know that I\'ve heard much in the way\n> of how we think *nature* picks which compactification...).\n\nIf you mean different topologies, it\'s okay, they are\nactually connected by CFTs with no geometrical interpretation\n(that\'s what all of this topology-change-in-string-theory\nstuff is about).\n\n> It\'s not global minima they\'re talking about here: I think it\'s\n> pretty well assumed that there are indeed globally\n> nonperturbatively stable SUSY vacua (11D Minkowski space,\n> for example), which would be global minima of the theory.\n\nYou are suggesting any universe ends up decompactifying to\n11 dimensions? At least for zero cosmological constant?\n\n> The 10^100 number is counting metastable vacua: SUSY\n> is broken in our world, so if the M-theory is the TOE, then\n> we\'re most likely in a metastable (but rather long lived)\n> "vacuum".\n\nWell, I think SUSY can be broken in a true vacuum as well.\nMost of the talk about we living in a metastable vacuum\ncomes from the fact the cosmological constant is positive,\nnot SUSY breaking - at least as far as I understand. Anyways,\nif you\'re right I don\'t see what all of that fuss about the\n"ugliness" of string theory and the need for the antropic\nprinciple is all about: it is then possible (even likely)\nthere are different regions of the universe which happen to\nbe near different local minima and we just happen to be in\nsome particular one.\n\n> I haven\'t heard one good\n> explanation of what happens in universes with *any*\n> positive value, but maybe I\'m just not as credulous as\n> I used to be when I was younger. ;)\n\nThe current wisdom is that they correspond to metastable\nstates in a universe with a negative or 0 cosmological\nconstant, apparently. A genuine de Sitter-type universe\nwould be likely to have a finite number of states because\nof the Bekenstein bound (if I understand correctly) and\nnobody knows how to construct such a sector of string theory.\n\nBest regards,\nSquark.\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Jake Mannix <jake@rset.net> wrote in message news:<12c1bbee.0405162054.3c204a65-100000@posting.google.com>...
> I'm no expert, but at least on this I think I can give you a little
> bit - if you're cool with the fact that the manifold M we
> compactify on has moduli (some related to things like its
> overall size or shape, and others related more to its
> analytic structure)
This is quite obvious, one can even express the local
dimension of the moduli space through the cohomology
dimensions of the CY.
> then once you put fluxes on M, the energy
> of the configuration should depend on moduli around which
> the fluxes are wrapped.
This is probably true, however, it seems unlikely that
alone would lead to a discrete set of (even local) minima.
Taking only that into account, one can always obtain an
infinity of equal-energy choices by rescaling the flux _and_
the moduli.
> > 1) How can this quantum potential be computer or merely
> > defined, at least in principle?
>
> So in particular choices of CY manifold to compactify on,
> you know what the moduli are, and as I parenthetically
> alluded to above, you sometimes have a good handle on
> "half" of the moduli, and can yes, see whether the moduli
> are lifted (and can then estimate, based on order of the
> equations defining the minima, the number of distinct
> vacua there are).
I still don't see how you actually compute the quantum
potential, except computing it for the effective QFT
approximation of theory. Well, I guess that's what they do...
> I'm still not sure how people go about
> picking what compactification to choose (well, more
> precisely, I don't know that I've heard much in the way
> of how we think *nature* picks which compactification...).
If you mean different topologies, it's okay, they are
actually connected by CFTs with no geometrical interpretation
(that's what all of this topology-change-in-string-theory
stuff is about).
> It's not global minima they're talking about here: I think it's
> pretty well assumed that there are indeed globally
> nonperturbatively stable SUSY vacua (11D Minkowski space,
> for example), which would be global minima of the theory.
You are suggesting any universe ends up decompactifying to
11 dimensions? At least for zero cosmological constant?
> The 10^100 number is counting metastable vacua: SUSY
> is broken in our world, so if the M-theory is the TOE, then
> we're most likely in a metastable (but rather long lived)
> "vacuum".
Well, I think SUSY can be broken in a true vacuum as well.
Most of the talk about we living in a metastable vacuum
comes from the fact the cosmological constant is positive,
not SUSY breaking - at least as far as I understand. Anyways,
if you're right I don't see what all of that fuss about the
"ugliness" of string theory and the need for the antropic
principle is all about: it is then possible (even likely)
there are different regions of the universe which happen to
be near different local minima and we just happen to be in
some particular one.
> I haven't heard one good
> explanation of what happens in universes with *any*
> positive value, but maybe I'm just not as credulous as
> I used to be when I was younger. ;)
The current wisdom is that they correspond to metastable
states in a universe with a negative or cosmological
constant, apparently. A genuine de Sitter-type universe
would be likely to have a finite number of states because
of the Bekenstein bound (if I understand correctly) and
nobody knows how to construct such a sector of string theory.
Best regards,
Squark.
Jake Mannix
May18-04, 06:10 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Squark <fiis5d@yahoo.com> wrote\n> Jake Mannix <jake@rset.net> wrote\n> > then once you put fluxes on M, the energy\n> > of the configuration should depend on moduli around which\n> > the fluxes are wrapped.\n>\n> This is probably true, however, it seems unlikely that\n> alone would lead to a discrete set of (even local) minima.\n> Taking only that into account, one can always obtain an\n> infinity of equal-energy choices by rescaling the flux _and_\n> the moduli.\n\nWhoa - if you ignore the fact that there are moduli at all,\nand consider that you\'ve got a fixed (moduli and all) CY you\'re\nconsidering, then saying you have some *integral* valued\nflux (fixed to be quantized by Dirac the quantization condition),\naren\'t you now forced to have a discrete set of choices for your\nflux?\n\nIf so, then you don\'t have *separate* moduli for the scale of\nthe fluxes and the moduli, and you can\'t independently rescale\nthem both.\n\n> > I\'m still not sure how people go about\n> > picking what compactification to choose (well, more\n> > precisely, I don\'t know that I\'ve heard much in the way\n> > of how we think *nature* picks which compactification...).\n>\n> If you mean different topologies, it\'s okay, they are\n> actually connected by CFTs with no geometrical interpretation\n> (that\'s what all of this topology-change-in-string-theory\n> stuff is about).\n\nOnce I understand what people mean by "nongeometric phases"\nof string theory, maybe I\'ll be able to really grok this, but at\npresent, I have no intuition for what this really means.\n\n> > It\'s not global minima they\'re talking about here: I think it\'s\n> > pretty well assumed that there are indeed globally\n> > nonperturbatively stable SUSY vacua (11D Minkowski space,\n> > for example), which would be global minima of the theory.\n>\n> You are suggesting any universe ends up decompactifying to\n> 11 dimensions? At least for zero cosmological constant?\n\nWell, I don\'t know if 11 is that important, but at least this\nrecent work of Giddings and Myers seems to be saying that\nfor *positive* CC, decompactification is always going to be\na problem: http://arxiv.org/abs/hep-th/0404220\n\nBut regardless, any vacuum with positive vacuum energy\nat a (local) minimum should be able to tunnel to one with\nzero vacuum energy, no? Independent of one\'s intepretation\nof the CC as a free parameter in the theory or as a\nrenormalized vacuum energy.\n\n> Well, I think SUSY can be broken in a true vacuum as well.\n\nHow do you mean? If the theory *has* SUSY minima, then\nany vacua with broken SUSY will have nonzero vacuum\nenergy, and hence be at best metastable, right? Or is this\nonly in global SUSY, and the SUGRA (or string theory) is\nmore tricky?\n\n> Most of the talk about we living in a metastable vacuum\n> comes from the fact the cosmological constant is positive,\n> not SUSY breaking - at least as far as I understand. Anyways,\n> if you\'re right I don\'t see what all of that fuss about the\n> "ugliness" of string theory and the need for the antropic\n> principle is all about: it is then possible (even likely)\n> there are different regions of the universe which happen to\n> be near different local minima and we just happen to be in\n> some particular one.\n\nI don\'t really feel qualified (philosophically or scientifically)\nto comment on anthropic arguments... so I\'ll try to leave\nmy personal bias out of this line of thinking. :)\n\n> The current wisdom is that they correspond to metastable\n> states in a universe with a negative or 0 cosmological\n> constant, apparently. A genuine de Sitter-type universe\n> would be likely to have a finite number of states because\n> of the Bekenstein bound (if I understand correctly) and\n> nobody knows how to construct such a sector of string theory.\n\nOther than the fact that we don\'t understand spatially compact\nspacetimes in quantum gravity, why are they thought to be\nmetastable? I\'ve heard reasonable arguments against the\nstability of de Sitter space at one time or another (something\nto do with infinite fragmentation due to topology changes in\nrandomly nulceated black holes, or something like that?), but\nI don\'t recall much of a general argument...\n\n-Jake Mannix\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Squark <fiis5d@yahoo.com> wrote
> Jake Mannix <jake@rset.net> wrote
> > then once you put fluxes on M, the energy
> > of the configuration should depend on moduli around which
> > the fluxes are wrapped.
>
> This is probably true, however, it seems unlikely that
> alone would lead to a discrete set of (even local) minima.
> Taking only that into account, one can always obtain an
> infinity of equal-energy choices by rescaling the flux _and_
> the moduli.
Whoa - if you ignore the fact that there are moduli at all,
and consider that you've got a fixed (moduli and all) CY you're
considering, then saying you have some *integral* valued
flux (fixed to be quantized by Dirac the quantization condition),
aren't you now forced to have a discrete set of choices for your
flux?
If so, then you don't have *separate* moduli for the scale of
the fluxes and the moduli, and you can't independently rescale
them both.
> > I'm still not sure how people go about
> > picking what compactification to choose (well, more
> > precisely, I don't know that I've heard much in the way
> > of how we think *nature* picks which compactification...).
>
> If you mean different topologies, it's okay, they are
> actually connected by CFTs with no geometrical interpretation
> (that's what all of this topology-change-in-string-theory
> stuff is about).
Once I understand what people mean by "nongeometric phases"
of string theory, maybe I'll be able to really grok this, but at
present, I have no intuition for what this really means.
> > It's not global minima they're talking about here: I think it's
> > pretty well assumed that there are indeed globally
> > nonperturbatively stable SUSY vacua (11D Minkowski space,
> > for example), which would be global minima of the theory.
>
> You are suggesting any universe ends up decompactifying to
> 11 dimensions? At least for zero cosmological constant?
Well, I don't know if 11 is that important, but at least this
recent work of Giddings and Myers seems to be saying that
for *positive* CC, decompactification is always going to be
a problem: http://arxiv.org/abs/http://www.arxiv.org/abs/hep-th/0404220
But regardless, any vacuum with positive vacuum energy
at a (local) minimum should be able to tunnel to one with
zero vacuum energy, no? Independent of one's intepretation
of the CC as a free parameter in the theory or as a
renormalized vacuum energy.
> Well, I think SUSY can be broken in a true vacuum as well.
How do you mean? If the theory *has* SUSY minima, then
any vacua with broken SUSY will have nonzero vacuum
energy, and hence be at best metastable, right? Or is this
only in global SUSY, and the SUGRA (or string theory) is
more tricky?
> Most of the talk about we living in a metastable vacuum
> comes from the fact the cosmological constant is positive,
> not SUSY breaking - at least as far as I understand. Anyways,
> if you're right I don't see what all of that fuss about the
> "ugliness" of string theory and the need for the antropic
> principle is all about: it is then possible (even likely)
> there are different regions of the universe which happen to
> be near different local minima and we just happen to be in
> some particular one.
I don't really feel qualified (philosophically or scientifically)
to comment on anthropic arguments... so I'll try to leave
my personal bias out of this line of thinking. :)
> The current wisdom is that they correspond to metastable
> states in a universe with a negative or cosmological
> constant, apparently. A genuine de Sitter-type universe
> would be likely to have a finite number of states because
> of the Bekenstein bound (if I understand correctly) and
> nobody knows how to construct such a sector of string theory.
Other than the fact that we don't understand spatially compact
spacetimes in quantum gravity, why are they thought to be
metastable? I've heard reasonable arguments against the
stability of de Sitter space at one time or another (something
to do with infinite fragmentation due to topology changes in
randomly nulceated black holes, or something like that?), but
I don't recall much of a general argument...
-Jake Mannix
Urs Schreiber
May18-04, 12:42 PM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>On Tue, 18 May 2004, Jake Mannix wrote:\n\n> Squark <fiis5d@yahoo.com> wrote\n\n> > If you mean different topologies, it\'s okay, they are\n> > actually connected by CFTs with no geometrical interpretation\n> > (that\'s what all of this topology-change-in-string-theory\n> > stuff is about).\n>\n> Once I understand what people mean by "nongeometric phases"\n> of string theory, maybe I\'ll be able to really grok this, but at\n> present, I have no intuition for what this really means.\n\nAs far as I know with the term "nongeometric phase" people usualy refer\nto string theory backgrounds (i.e. to (S)CFTs) which do not have an\ninterpretation as a sigma-model on the worldsheet.\n\nBut I wonder if this is really what Squark meant, because it seemed\nto me that he was rather referring to flop transitions, or something\nlike that. (But maybe the two concepts are related, I don\'t know\nmuch about this.)\n\n> Independent of one\'s intepretation\n> of the CC as a free parameter in the theory or as a\n> renormalized vacuum energy.\n\nBTW, how is this "interpretation" dealt with in string theory, really?\nCan we identify a contribution to the CC from the effective field 0-modes?\n\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>On Tue, 18 May 2004, Jake Mannix wrote:
> Squark <fiis5d@yahoo.com> wrote
> > If you mean different topologies, it's okay, they are
> > actually connected by CFTs with no geometrical interpretation
> > (that's what all of this topology-change-in-string-theory
> > stuff is about).
>
> Once I understand what people mean by "nongeometric phases"
> of string theory, maybe I'll be able to really grok this, but at
> present, I have no intuition for what this really means.
As far as I know with the term "nongeometric phase" people usualy refer
to string theory backgrounds (i.e. to (S)CFTs) which do not have an
interpretation as a \sigma-model on the worldsheet.
But I wonder if this is really what Squark meant, because it seemed
to me that he was rather referring to flop transitions, or something
like that. (But maybe the two concepts are related, I don't know
much about this.)
> Independent of one's intepretation
> of the CC as a free parameter in the theory or as a
> renormalized vacuum energy.
BTW, how is this "interpretation" dealt with in string theory, really?
Can we identify a contribution to the CC from the effective field 0-modes?
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Jake Mannix <jake@rset.net> wrote in message news:<12c1bbee.0405180145.3ba7bfaf-100000@posting.google.com>...\n> Whoa - if you ignore the fact that there are moduli at all,\n> and consider that you\'ve got a fixed (moduli and all) CY you\'re\n> considering, then saying you have some *integral* valued\n> flux (fixed to be quantized by Dirac the quantization condition),\n> aren\'t you now forced to have a discrete set of choices for your\n> flux?\n\nFirstly, I wonder what people mean by "flux" in the context.\nThe massless fields you have (except the metric) are the\nNS-NS 2-form B and the R-R k-forms C_k (k even for IIB and\nodd for IIA type theory). If you put a flat form on the CY,\nit wouldn\'t result in any moduli-dependance of the energy.\nOTOH, if you allow for curvature the compactification\nmanifold would have to have a non-vanishing Ricci tensor\nand it would no longer be CY. So, stricticly speaking, it\'s\nnot clear the CY moduli are meaningful in the context.\nSecondly, there is no quantization condition here, as far\nas I can tell. A la contraire, you should consider the\nspace of forms modulo flat integral forms since this cause\nno effect even on the quantum level.\nThirdly, it still appears that by adding the fluxes you\nadded as many variables as equations, hence the solution\nspace hasn\'t become discretely.\nFourthly, I don\'t see how any of these arguments can rule\nout the zero-flux vacua unless the quantum potential can\nactually be decreased (in all but a discrete subset of\nthe cases) by adding flux, which deserves explanation.\n\n> Once I understand what people mean by "nongeometric phases"\n> of string theory, maybe I\'ll be able to really grok this, but at\n> present, I have no intuition for what this really means.\n\nRoughly, the idea is as follows: string theory\ncompactified on a Calabi-Yau is the product of two CFTs,\none a 4D sigma model and the second a 6D non-linear sigma\nmodel. Now, you can think of it that any CY manifold\ncorresponds to a point at the "moduli space of CFTs".\nContinuously deforming the CY changes that point\ncontinuously. However, CYs which are not connected by any\ncontinuous deformation may still be connected by a path\nin the "moduli space of CFTs". This path would have to\ncross points which don\'t correspond to a non-linear sigma\nmodel with _any_ target space but still correspond to\nsome "abstract" CFT. More or less, the result is a string\nin 4D spacetime with additional quantum fields on the\nworldsheet which have no non-linear-sigma-model\ninterpretation. I\'m not even sure these fields may be\ndescribed via a classical Lagrangian - it\'s an interesting\nquestion whether they can.\nThe simplest example is so-called "flop transitions" when\na CY modulus becomes negative (something which has no\nmeaning geometrically) in effect moving us to a CY with\na different topology. In this case the two topologies are\ndifferent blow-ups (smooth resolutions) of the singular\nmanifold resulting at the vanishing modulus point.\n\n> But regardless, any vacuum with positive vacuum energy\n> at a (local) minimum should be able to tunnel to one with\n> zero vacuum energy, no? Independent of one\'s intepretation\n> of the CC as a free parameter in the theory or as a\n> renormalized vacuum energy.\n\nI\'m not sure this is true if the vacua correspond to different\ncosmological constant. The QFT intuition can well go wrong\nhere since the asymptotic form of spacetime is completely\ndifferent and it\'s not clear whether the two vacua can be\nthought of as "different sectors of the same theory".\n\n> How do you mean? If the theory *has* SUSY minima, then\n> any vacua with broken SUSY will have nonzero vacuum\n> energy, and hence be at best metastable, right? Or is this\n> only in global SUSY, and the SUGRA (or string theory) is\n> more tricky?\n\nI don\'t think it\'s right. It might be true in QFT, or at\nleast most QFTs but I don\'t think it follows from the\nSuperPoincare group representation theory, so there\'s no\napparent reason it would hold in string theory.\n\n> Other than the fact that we don\'t understand spatially compact\n> spacetimes in quantum gravity, why are they thought to be\n> metastable?\n\nSimple: metastable de Sitter sectors of string theory have\nbeen constructed. They are clearly metastable as they live\nin a local-only minimum of the quantum potential. No true\n(stable) de Sitter vacuum has been constructed so far.\n\nBest regards,\nSquark.\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Jake Mannix <jake@rset.net> wrote in message news:<12c1bbee.0405180145.3ba7bfaf-100000@posting.google.com>...
> Whoa - if you ignore the fact that there are moduli at all,
> and consider that you've got a fixed (moduli and all) CY you're
> considering, then saying you have some *integral* valued
> flux (fixed to be quantized by Dirac the quantization condition),
> aren't you now forced to have a discrete set of choices for your
> flux?
Firstly, I wonder what people mean by "flux" in the context.
The massless fields you have (except the metric) are the
NS-NS 2-form B and the R-R k-forms C_k (k even for IIB and
odd for IIA type theory). If you put a flat form on the CY,
it wouldn't result in any moduli-dependance of the energy.
OTOH, if you allow for curvature the compactification
manifold would have to have a non-vanishing Ricci tensor
and it would no longer be CY. So, stricticly speaking, it's
not clear the CY moduli are meaningful in the context.
Secondly, there is no quantization condition here, as far
as I can tell. A la contraire, you should consider the
space of forms modulo flat integral forms since this cause
no effect even on the quantum level.
Thirdly, it still appears that by adding the fluxes you
added as many variables as equations, hence the solution
space hasn't become discretely.
Fourthly, I don't see how any of these arguments can rule
out the zero-flux vacua unless the quantum potential can
actually be decreased (in all but a discrete subset of
the cases) by adding flux, which deserves explanation.
> Once I understand what people mean by "nongeometric phases"
> of string theory, maybe I'll be able to really grok this, but at
> present, I have no intuition for what this really means.
Roughly, the idea is as follows: string theory
compactified on a Calabi-Yau is the product of two CFTs,
one a 4D \sigma model and the second a 6D non-linear \sigma
model. Now, you can think of it that any CY manifold
corresponds to a point at the "moduli space of CFTs".
Continuously deforming the CY changes that point
continuously. However, CYs which are not connected by any
continuous deformation may still be connected by a path
in the "moduli space of CFTs". This path would have to
cross points which don't correspond to a non-linear \sigma
model with _any_ target space but still correspond to
some "abstract" CFT. More or less, the result is a string
in 4D spacetime with additional quantum fields on the
worldsheet which have no non-linear-\sigma-model
interpretation. I'm not even sure these fields may be
described via a classical Lagrangian - it's an interesting
question whether they can.
The simplest example is so-called "flop transitions" when
a CY modulus becomes negative (something which has no
meaning geometrically) in effect moving us to a CY with
a different topology. In this case the two topologies are
different blow-ups (smooth resolutions) of the singular
manifold resulting at the vanishing modulus point.
> But regardless, any vacuum with positive vacuum energy
> at a (local) minimum should be able to tunnel to one with
> zero vacuum energy, no? Independent of one's intepretation
> of the CC as a free parameter in the theory or as a
> renormalized vacuum energy.
I'm not sure this is true if the vacua correspond to different
cosmological constant. The QFT intuition can well go wrong
here since the asymptotic form of spacetime is completely
different and it's not clear whether the two vacua can be
thought of as "different sectors of the same theory".
> How do you mean? If the theory *has* SUSY minima, then
> any vacua with broken SUSY will have nonzero vacuum
> energy, and hence be at best metastable, right? Or is this
> only in global SUSY, and the SUGRA (or string theory) is
> more tricky?
I don't think it's right. It might be true in QFT, or at
least most QFTs but I don't think it follows from the
SuperPoincare group representation theory, so there's no
apparent reason it would hold in string theory.
> Other than the fact that we don't understand spatially compact
> spacetimes in quantum gravity, why are they thought to be
> metastable?
Simple: metastable de Sitter sectors of string theory have
been constructed. They are clearly metastable as they live
in a local-only minimum of the quantum potential. No true
(stable) de Sitter vacuum has been constructed so far.
Best regards,
Squark.
Jake Mannix
May19-04, 04:08 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Squark <fiis5d@yahoo.com> wrote\n> Firstly, I wonder what people mean by "flux" in the context.\n> The massless fields you have (except the metric) are the\n> NS-NS 2-form B and the R-R k-forms C_k (k even for IIB and\n> odd for IIA type theory).\n\nYeah, these are the forms that are used - if they (or more\naccurately, their field strengths) are chosen to take values in\nH^p(M,Z) (where M is the CY in question), you\'re constructing\na \'flux compactification\'. It seems to be important that the\nfluxes are integral valued, without this, I can\'t imagine how\nany discrete number comes out of these countings.\n\n> If you put a flat form on the CY,\n> it wouldn\'t result in any moduli-dependance of the energy.\n\nAccording to Taylor and Vafa (hep-th/9912152), page 5, in\nthe case of the two different 3-form field strengths of IIB,\nH_RR and H_NS, turning on these fluxes generates a\nsuperpotential W = \\int_M { \\Omega ^ (\\tau*H_NS + H_RR) }\nwhere \\Omega is the holomorphic 3-form of the CY, and \\tau\nis the complexified string coupling.\n\nWhat confuses me is that it seems you should be turning on\n*magnetic* fluxes, so that the forms are still flat, but nontrivial\ndue to the topology. Maybe clearing this up would also show\nus where the quantization condition is coming from.\n\n> Fourthly, I don\'t see how any of these arguments can rule\n> out the zero-flux vacua unless the quantum potential can\n> actually be decreased (in all but a discrete subset of\n> the cases) by adding flux, which deserves explanation.\n\nI don\'t think these arguments are meant to rule out the\nzero flux vacua - the huge discrete set of vacua aren\'t in\ngeneral at all meant to say these are the *only* vacua - as\nwe discussed before, there\'s certainly still the flat Minkowski\nsolution that\'s not getting ruled out - we\'re just looking for\nvacua which look like they can reproduce the real world.\n\n<snipped nice explanation of topology change CFTs, thanks>\n\n> I\'m not sure this is true if the vacua correspond to different\n> cosmological constant. The QFT intuition can well go wrong\n> here since the asymptotic form of spacetime is completely\n> different and it\'s not clear whether the two vacua can be\n> thought of as "different sectors of the same theory".\n\nI\'m not sure I understand what you mean here - aren\'t we\nsaying the same thing? That we don\'t currently know if the\nCC is a free parameter (which may be modified by quantum\ncorrections, but it may be free other than that), or if it\'s\nfixed by the theory (or at least the theory and the choice of\nvacuum - by QFT-like intuition where it just comes from\nvacuum energy from the value of the potential).\n\n----\n\nWell, I was hoping some of the more experienced stringy\nfolk who are active here would jump in and fix up our\nunderstanding of this flux vacuum business, because I\ncan\'t seem to find a really comprehensive and/or readable\nintroduction to them on the archives, and I\'m really going\nbased on just a few talks on this I\'ve seen, and sifting\nthrough papers of Douglas, Vafa, Kachru, etc.\n\nLubos, or someone else - care to point out a good review\non this?\n\n-Jake Mannix\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Squark <fiis5d@yahoo.com> wrote
> Firstly, I wonder what people mean by "flux" in the context.
> The massless fields you have (except the metric) are the
> NS-NS 2-form B and the R-R k-forms C_k (k even for IIB and
> odd for IIA type theory).
Yeah, these are the forms that are used - if they (or more
accurately, their field strengths) are chosen to take values in
H^p(M,Z) (where M is the CY in question), you're constructing
a 'flux compactification'. It seems to be important that the
fluxes are integral valued, without this, I can't imagine how
any discrete number comes out of these countings.
> If you put a flat form on the CY,
> it wouldn't result in any moduli-dependance of the energy.
According to Taylor and Vafa (http://www.arxiv.org/abs/hep-th/9912152), page 5, in
the case of the two different 3-form field strengths of IIB,
H_{RR} and H_{NS}, turning on these fluxes generates a
superpotential W = \int_M { \Omega ^ (\tau*H_{NS} + H_{RR}) }
where \Omega is the holomorphic 3-form of the CY, and \tau
is the complexified string coupling.
What confuses me is that it seems you should be turning on
*magnetic* fluxes, so that the forms are still flat, but nontrivial
due to the topology. Maybe clearing this up would also show
us where the quantization condition is coming from.
> Fourthly, I don't see how any of these arguments can rule
> out the zero-flux vacua unless the quantum potential can
> actually be decreased (in all but a discrete subset of
> the cases) by adding flux, which deserves explanation.
I don't think these arguments are meant to rule out the
zero flux vacua - the huge discrete set of vacua aren't in
general at all meant to say these are the *only* vacua - as
we discussed before, there's certainly still the flat Minkowski
solution that's not getting ruled out - we're just looking for
vacua which look like they can reproduce the real world.
<snipped nice explanation of topology change CFTs, thanks>
> I'm not sure this is true if the vacua correspond to different
> cosmological constant. The QFT intuition can well go wrong
> here since the asymptotic form of spacetime is completely
> different and it's not clear whether the two vacua can be
> thought of as "different sectors of the same theory".
I'm not sure I understand what you mean here - aren't we
saying the same thing? That we don't currently know if the
CC is a free parameter (which may be modified by quantum
corrections, but it may be free other than that), or if it's
fixed by the theory (or at least the theory and the choice of
vacuum - by QFT-like intuition where it just comes from
vacuum energy from the value of the potential).
----
Well, I was hoping some of the more experienced stringy
folk who are active here would jump in and fix up our
understanding of this flux vacuum business, because I
can't seem to find a really comprehensive and/or readable
introduction to them on the archives, and I'm really going
based on just a few talks on this I've seen, and sifting
through papers of Douglas, Vafa, Kachru, etc.
Lubos, or someone else - care to point out a good review
on this?
-Jake Mannix
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Jake Mannix <jake@rset.net> wrote in message news:<12c1bbee.0405182240.2da0b8fc-100000@posting.google.com>...\n\n> What confuses me is that it seems you should be turning on\n> *magnetic* fluxes, so that the forms are still flat, but nontrivial\n> due to the topology. Maybe clearing this up would also show\n> us where the quantization condition is coming from.\n\nOk, you are partly right. Our n-forms should be replaced by\nconnections on a non-trivial n-gerb. The field strengths\n(which are locally the differentials of the n-forms) are then\nclosed but not necassarily exact and indeed correspond to\nintegral cohomology elements. This is perfectly analogical\nto ordinary connection where the curvature form\'s cohomology\nis the 2nd Chern class of the bundle which is, of course,\nintegral.\n\n> I don\'t think these arguments are meant to rule out the\n> zero flux vacua - the huge discrete set of vacua aren\'t in\n> general at all meant to say these are the *only* vacua - as\n> we discussed before, there\'s certainly still the flat Minkowski\n> solution that\'s not getting ruled out - we\'re just looking for\n> vacua which look like they can reproduce the real world.\n\nIn fact, it is possible only a finite set of cohomology\nclasses have associated stable vacua (global minima of the\nquantum potential). I don\'t know why it should be like that,\nbut it might be. Zero flux may also correspond to a stable\nvacuum: or it may not. alpha\' corrections should generate\na non-trivial quantum potential for the moduli in the zero\nflux sector as well, since there\'s no symmetry that would\nprotect against it. For cohomology classes with no stable\nvacuum we probably get decompactification.\nThe thing I still don\'t understand is how to define the\nquantum potential in string theory. I also don\'t understand\nwhether anyone understands it, and whether it is actually\ndefined rather than just being an approximation our QFT\nintuition is sympathetic with. hep-th/0204027 seems to\nsuggest the later.\n\n> I\'m not sure I understand what you mean here - aren\'t we\n> saying the same thing? That we don\'t currently know if the\n> CC is a free parameter (which may be modified by quantum\n> corrections, but it may be free other than that), or if it\'s\n> fixed by the theory (or at least the theory and the choice of\n> vacuum - by QFT-like intuition where it just comes from\n> vacuum energy from the value of the potential).\n\nWell, as far as I understand the situation is as follows: there\nare stable superstring vacua for certain (I don\'t know which,\nand whether all or not) non-positive values of the CC. Each of\nthese vacuum sectors may contain false vacua with CC of either\nsign.\n\nBest regards,\nSquark.\n\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Jake Mannix <jake@rset.net> wrote in message news:<12c1bbee.0405182240.2da0b8fc-100000@posting.google.com>...
> What confuses me is that it seems you should be turning on
> *magnetic* fluxes, so that the forms are still flat, but nontrivial
> due to the topology. Maybe clearing this up would also show
> us where the quantization condition is coming from.
Ok, you are partly right. Our n-forms should be replaced by
connections on a non-trivial n-gerb. The field strengths
(which are locally the differentials of the n-forms) are then
closed but not necassarily exact and indeed correspond to
integral cohomology elements. This is perfectly analogical
to ordinary connection where the curvature form's cohomology
is the 2nd Chern class of the bundle which is, of course,
integral.
> I don't think these arguments are meant to rule out the
> zero flux vacua - the huge discrete set of vacua aren't in
> general at all meant to say these are the *only* vacua - as
> we discussed before, there's certainly still the flat Minkowski
> solution that's not getting ruled out - we're just looking for
> vacua which look like they can reproduce the real world.
In fact, it is possible only a finite set of cohomology
classes have associated stable vacua (global minima of the
quantum potential). I don't know why it should be like that,
but it might be. Zero flux may also correspond to a stable
vacuum: or it may not. \alpha' corrections should generate
a non-trivial quantum potential for the moduli in the zero
flux sector as well, since there's no symmetry that would
protect against it. For cohomology classes with no stable
vacuum we probably get decompactification.
The thing I still don't understand is how to define the
quantum potential in string theory. I also don't understand
whether anyone understands it, and whether it is actually
defined rather than just being an approximation our QFT
intuition is sympathetic with. http://www.arxiv.org/abs/hep-th/0204027 seems to
suggest the later.
> I'm not sure I understand what you mean here - aren't we
> saying the same thing? That we don't currently know if the
> CC is a free parameter (which may be modified by quantum
> corrections, but it may be free other than that), or if it's
> fixed by the theory (or at least the theory and the choice of
> vacuum - by QFT-like intuition where it just comes from
> vacuum energy from the value of the potential).
Well, as far as I understand the situation is as follows: there
are stable superstring vacua for certain (I don't know which,
and whether all or not) non-positive values of the CC. Each of
these vacuum sectors may contain false vacua with CC of either
sign.
Best regards,
Squark.
Jake Mannix
May20-04, 06:29 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Squark said:\n\n> In fact, it is possible only a finite set of cohomology\n> classes have associated stable vacua (global minima of the\n> quantum potential). I don\'t know why it should be like that,\n> but it might be.\n\nI really don\'t think when people are talking about these\nflux vacua where the moduli have all been lifted that they\'re\ntalking about *global* minima - I don\'t see why a gazillion\ndifferent local minima which pop up would end up all having\nthe same value for the height of the potential there (unless\nrelated by a [super- or otherwise] symmetry).\n\n> Zero flux may also correspond to a stable\n> vacuum: or it may not. alpha\' corrections should generate\n> a non-trivial quantum potential for the moduli in the zero\n> flux sector as well, since there\'s no symmetry that would\n> protect against it.\n\nHmm... I guess I can\'t recall any argument against maximal\nSUGRA generating nonperturbative potentials (since I\'m not\nreally going to trust my stringy intuition, as it\'s practically\nnonexistent, I\'ll stick to the low-energy effective field theory),\nso I guess I\'ll have to concede this.\n\nBut I\'ve never heard much in the way of people wondering\nabout the stability of the "really simple vacuua", so I\'ll guess\nthat either it\'s for some reason much much harder than\nthe nontrivial flux case, or it\'s pretty easy to show that it\ndoes indeed seem stable.\n\n> For cohomology classes with no stable\n> vacuum we probably get decompactification.\n\nAnd if we\'re already fully decompactified?\n\n> The thing I still don\'t understand is how to define the\n> quantum potential in string theory. I also don\'t understand\n> whether anyone understands it, and whether it is actually\n> defined rather than just being an approximation our QFT\n> intuition is sympathetic with. hep-th/0204027 seems to\n> suggest the later.\n\n*Define*, or "know how to calculate"? It seems that just\nas in a strongly coupled QFT, we may have no idea of its form,\nunless symmetry helps us in some way, or there\'s some\ntechnical tool handy, but it\'s still totally sensible to talk\nabout in the usual way.\n\n> Well, as far as I understand the situation is as follows: there\n> are stable superstring vacua for certain (I don\'t know which,\n> and whether all or not) non-positive values of the CC. Each of\n> these vacuum sectors may contain false vacua with CC of either\n> sign.\n\nDo you know how they are known to be nonperturbatively stable?\nAnd what does it mean to tunnel from a vacuum with one value of\nthe CC to another, and how is this different from the naive\nunderstanding of the CC as just being the vacuum energy value?\n\n-Jake Mannix\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Squark said:
> In fact, it is possible only a finite set of cohomology
> classes have associated stable vacua (global minima of the
> quantum potential). I don't know why it should be like that,
> but it might be.
I really don't think when people are talking about these
flux vacua where the moduli have all been lifted that they're
talking about *global* minima - I don't see why a gazillion
different local minima which pop up would end up all having
the same value for the height of the potential there (unless
related by a [super- or otherwise] symmetry).
> Zero flux may also correspond to a stable
> vacuum: or it may not. \alpha' corrections should generate
> a non-trivial quantum potential for the moduli in the zero
> flux sector as well, since there's no symmetry that would
> protect against it.
Hmm... I guess I can't recall any argument against maximal
SUGRA generating nonperturbative potentials (since I'm not
really going to trust my stringy intuition, as it's practically
nonexistent, I'll stick to the low-energy effective field theory),
so I guess I'll have to concede this.
But I've never heard much in the way of people wondering
about the stability of the "really simple vacuua", so I'll guess
that either it's for some reason much much harder than
the nontrivial flux case, or it's pretty easy to show that it
does indeed seem stable.
> For cohomology classes with no stable
> vacuum we probably get decompactification.
And if we're already fully decompactified?
> The thing I still don't understand is how to define the
> quantum potential in string theory. I also don't understand
> whether anyone understands it, and whether it is actually
> defined rather than just being an approximation our QFT
> intuition is sympathetic with. http://www.arxiv.org/abs/hep-th/0204027 seems to
> suggest the later.
*Define*, or "know how to calculate"? It seems that just
as in a strongly coupled QFT, we may have no idea of its form,
unless symmetry helps us in some way, or there's some
technical tool handy, but it's still totally sensible to talk
about in the usual way.
> Well, as far as I understand the situation is as follows: there
> are stable superstring vacua for certain (I don't know which,
> and whether all or not) non-positive values of the CC. Each of
> these vacuum sectors may contain false vacua with CC of either
> sign.
Do you know how they are known to be nonperturbatively stable?
And what does it mean to tunnel from a vacuum with one value of
the CC to another, and how is this different from the naive
understanding of the CC as just being the vacuum energy value?
-Jake Mannix
Charlie Stromeyer Jr.
May20-04, 06:46 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Jake Mannix <jake@rset.net> wrote in message news:\n\n> Well, I was hoping some of the more experienced stringy\n> folk who are active here would jump in and fix up our\n> understanding of this flux vacuum business, because I\n> can\'t seem to find a really comprehensive and/or readable\n> introduction to them on the archives, and I\'m really going\n> based on just a few talks on this I\'ve seen, and sifting\n> through papers of Douglas, Vafa, Kachru, etc.\n>\n> Lubos, or someone else - care to point out a good review\n> on this?\n\nI am not aware of a good review on this subject and I suspect that you\nwill not find any because the topic is too difficult and complicated,\nalthough there is a recent preprint about some taxonomy of flux vacua\n[1].\n\nHowever, I personally believe that it would be much more preferable\nfor us to first heed a remark that Lubos Motl once made over in s.p.r.\nbecause I feel that his remark was very insightful and implicitly\nuseful advice, even though I am sure that he is not the first person\nto have made such a remark. Here, I am only roughly paraphrasing what\nI remember to be what Lubos wrote:\n\n"It would have been a large waste of time for some 19th century\nphysicists to have used Newton\'s equations in an attempt to calculate\nthe expansion of the universe instead of first waiting for the\nnecessary foundational framework, which of course was GTR."\n\nWhen I read this remark I almost slapped my own forehead :-) because\nI interpreted this remark as a succinct expression of my own\nintuitions at the time that some string theorists may have been overly\nspeculating about dS spacetimes, large extra dimensions, too many\ndifferent vacua, etc. instead of first trying to gain a better\nunderstanding of what I felt would more likely be something like\nunderlying and foundational principles or concepts.\n\nLet us each thank Lubos for his remark and then make sure that we do\nnot forget it!\n\n\n[1] http://arxiv.org/abs/hep-th/0404243\n\n\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Jake Mannix <jake@rset.net> wrote in message news:
> Well, I was hoping some of the more experienced stringy
> folk who are active here would jump in and fix up our
> understanding of this flux vacuum business, because I
> can't seem to find a really comprehensive and/or readable
> introduction to them on the archives, and I'm really going
> based on just a few talks on this I've seen, and sifting
> through papers of Douglas, Vafa, Kachru, etc.
>
> Lubos, or someone else - care to point out a good review
> on this?
I am not aware of a good review on this subject and I suspect that you
will not find any because the topic is too difficult and complicated,
although there is a recent preprint about some taxonomy of flux vacua
[1].
However, I personally believe that it would be much more preferable
for us to first heed a remark that Lubos Motl once made over in s.p.r.
because I feel that his remark was very insightful and implicitly
useful advice, even though I am sure that he is not the first person
to have made such a remark. Here, I am only roughly paraphrasing what
I remember to be what Lubos wrote:
"It would have been a large waste of time for some 19th century
physicists to have used Newton's equations in an attempt to calculate
the expansion of the universe instead of first waiting for the
necessary foundational framework, which of course was GTR."
When I read this remark I almost slapped my own forehead :-) because
I interpreted this remark as a succinct expression of my own
intuitions at the time that some string theorists may have been overly
speculating about dS spacetimes, large extra dimensions, too many
different vacua, etc. instead of first trying to gain a better
understanding of what I felt would more likely be something like
underlying and foundational principles or concepts.
Let us each thank Lubos for his remark and then make sure that we do
not forget it!
[1] http://arxiv.org/abs/http://www.arxiv.org/abs/hep-th/0404243
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Jake Mannix <jake@rset.net> wrote in message news:<12c1bbee.0405200102.6e3b58fe-100000@posting.google.com>...\n> I really don\'t think when people are talking about these\n> flux vacua where the moduli have all been lifted that they\'re\n> talking about *global* minima - I don\'t see why a gazillion\n> different local minima which pop up would end up all having\n> the same value for the height of the potential there (unless\n> related by a [super- or otherwise] symmetry).\n\nBtw, if they _were_ related by a symmetry, they would all be\nphysically equivalent anyway. However, you are missing my\npoint. What I\'m saying is that the H^k(X, Z) charges associated\nwith the fluxes are conserved, therefore, a global minima of\nthe quantum potential _costrained to a single value of these\ncharges_ corresponds to a stable vacuum. Such a plethora of\nstable vacua can appear already in ordinary gauge theory on a\nspacetime of the form M x X where M is ordinary Minkowski space\nand X is a compact manifold with nontrivial H^2(X, G), G being\nthe gauge group.\n\n> Hmm... I guess I can\'t recall any argument against maximal\n> SUGRA generating nonperturbative potentials (since I\'m not\n> really going to trust my stringy intuition, as it\'s practically\n> nonexistent, I\'ll stick to the low-energy effective field theory),\n> so I guess I\'ll have to concede this.\n\nIn fact, it appear likely for a quantum potential\nto appear already on the perturbative level. In\nthe same way it would happen in QED with charged\nmassless scalars, say.\n\n> But I\'ve never heard much in the way of people wondering\n> about the stability of the "really simple vacuua", so I\'ll guess\n> that either it\'s for some reason much much harder than\n> the nontrivial flux case, or it\'s pretty easy to show that it\n> does indeed seem stable.\n\nWell, the only really simple vacua I know are the\n11D Minkowski space of M-theory and 5 10D string\ntheories. The former probably just doesn\'t have\nany exciation that can possibly unstabilize it.\nThe later have the dilaton, but I guess there must\nbe some simple argument why it can\'t "go wild"\n(for type IIA it would mean decompactification\ninto 11 dimensions!), I dunno.\n\n> > For cohomology classes with no stable\n> > vacuum we probably get decompactification.\n>\n> And if we\'re already fully decompactified?\n\nWhy decompactified? We are compactified to 4\ndimensions, like we should be. At least _I_\nam, you never know with the internet... ;-)\n\n> *Define*, or "know how to calculate"?\n\nDefine. In QFT the quantum potential is essentially\nthe static part of the quantum effective action,\nwhereas the later is defined to be a Legendre\ntransform of the generating functional. In string\ntheory there\'s no generating functional as far as\nanybody knows (I think), there\'s only the S-matrix.\n\n> Do you know how they are known to be nonperturbatively stable?\n\nWell, for negative CC we have AdS/CFT which seems\nto imply there is a stable vacuum, since there\nis one in the CFT. I don\'t know how to reconcile\nthis with the claim the CC might be quantized\nappearing in hep-th/0204027, though. I don\'t think\nanyone _knows_ a zero CC 4D "vacuum contender" to\nbe nonperturbatively stable, I suppose they\'re\njust making educated guessing...\n\n> And what does it mean to tunnel from a vacuum with one value of\n> the CC to another, and how is this different from the naive\n> understanding of the CC as just being the vacuum energy value?\n\nNo idea. I\'m not sure anybody understands that.\n\nBest regards,\nSquark.\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Jake Mannix <jake@rset.net> wrote in message news:<12c1bbee.0405200102.6e3b58fe-100000@posting.google.com>...
> I really don't think when people are talking about these
> flux vacua where the moduli have all been lifted that they're
> talking about *global* minima - I don't see why a gazillion
> different local minima which pop up would end up all having
> the same value for the height of the potential there (unless
> related by a [super- or otherwise] symmetry).
Btw, if they _were_ related by a symmetry, they would all be
physically equivalent anyway. However, you are missing my
point. What I'm saying is that the H^k(X, Z) charges associated
with the fluxes are conserved, therefore, a global minima of
the quantum potential _costrained to a single value of these
charges_ corresponds to a stable vacuum. Such a plethora of
stable vacua can appear already in ordinary gauge theory on a
spacetime of the form M x X where M is ordinary Minkowski space
and X is a compact manifold with nontrivial H^2(X, G), G being
the gauge group.
> Hmm... I guess I can't recall any argument against maximal
> SUGRA generating nonperturbative potentials (since I'm not
> really going to trust my stringy intuition, as it's practically
> nonexistent, I'll stick to the low-energy effective field theory),
> so I guess I'll have to concede this.
In fact, it appear likely for a quantum potential
to appear already on the perturbative level. In
the same way it would happen in QED with charged
massless scalars, say.
> But I've never heard much in the way of people wondering
> about the stability of the "really simple vacuua", so I'll guess
> that either it's for some reason much much harder than
> the nontrivial flux case, or it's pretty easy to show that it
> does indeed seem stable.
Well, the only really simple vacua I know are the
11D Minkowski space of M-theory and 5 10D string
theories. The former probably just doesn't have
any exciation that can possibly unstabilize it.
The later have the dilaton, but I guess there must
be some simple argument why it can't "go wild"
(for type IIA it would mean decompactification
into 11 dimensions!), I dunno.
> > For cohomology classes with no stable
> > vacuum we probably get decompactification.
>
> And if we're already fully decompactified?
Why decompactified? We are compactified to 4
dimensions, like we should be. At least _I_
am, you never know with the internet... ;-)
> *Define*, or "know how to calculate"?
Define. In QFT the quantum potential is essentially
the static part of the quantum effective action,
whereas the later is defined to be a Legendre
transform of the generating functional. In string
theory there's no generating functional as far as
anybody knows (I think), there's only the S-matrix.
> Do you know how they are known to be nonperturbatively stable?
Well, for negative CC we have AdS/CFT which seems
to imply there is a stable vacuum, since there
is one in the CFT. I don't know how to reconcile
this with the claim the CC might be quantized
appearing in http://www.arxiv.org/abs/hep-th/0204027, though. I don't think
anyone _knows_ a zero CC 4D "vacuum contender" to
be nonperturbatively stable, I suppose they're
just making educated guessing...
> And what does it mean to tunnel from a vacuum with one value of
> the CC to another, and how is this different from the naive
> understanding of the CC as just being the vacuum energy value?
No idea. I'm not sure anybody understands that.
Best regards,
Squark.
Jake Mannix
May21-04, 02:04 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Squark <fiis5d@yahoo.com> wrote\n> Well, the only really simple vacua I know are the\n> 11D Minkowski space of M-theory and 5 10D string\n> theories. The former probably just doesn\'t have\n> any exciation that can possibly unstabilize it.\n> The later have the dilaton, but I guess there must\n> be some simple argument why it can\'t "go wild"\n> (for type IIA it would mean decompactification\n> into 11 dimensions!), I dunno.\n\nRight, and I was thinking of the really simple\ncompactifications of these - like the maximal\nSUSY preserving toroidal kind, or AdS x S kind.\n\n> > > For cohomology classes with no stable\n> > > vacuum we probably get decompactification.\n> >\n> > And if we\'re already fully decompactified?\n>\n> Why decompactified? We are compactified to 4\n> dimensions, like we should be. At least _I_\n> am, you never know with the internet... ;-)\n\nHeh - I\'m think we just ended up talking at angles\na litte bit - I was considering *any* possible vacuum,\nnot just the ones which have a M_4 x CY\ndecomposition, for the purposes of the argument\non "which vacuua do we know are stable/metastable".\n\nThese other vacuua (11 or 10D minkowski, or\nputting those on a torus, yeilding way too much SUSY,\netc...) aren\'t reasonable candidates for *our* vacuum,\nbut they\'re still interesting to consider as for their\nfate, and their "altitude" on the landscape, for\nthe purposes of seeing whether we can tunnel from\nhere to there from one of the CY-flux vacua.\n\n> > *Define*, or "know how to calculate"?\n>\n> Define. In QFT the quantum potential is essentially\n> the static part of the quantum effective action,\n> whereas the later is defined to be a Legendre\n> transform of the generating functional. In string\n> theory there\'s no generating functional as far as\n> anybody knows (I think), there\'s only the S-matrix.\n\nRight, well I think much of the arguments I\'ve read\nhave boiled down to SUGRA thinking: at tree level\nin g_string, but allowing for higher order in \\alpha\'.\n\n> > Do you know how they are known to be nonperturbatively stable?\n>\n> Well, for negative CC we have AdS/CFT which seems\n> to imply there is a stable vacuum, since there\n> is one in the CFT.\n\nWell, as long as we believe that N=4 SYM is really even\nwell defined in the first place - it\'s not asymptotically\nfree, so what do you mean by a nonperturbative microscopic\ndefinition of the theory? I\'m being a little bit nitpicky here,\nbecause I think there probably is a nice way to embed N=4\nin an asymptotically free SYM such that you could have a\nfree microscopic definition, if you (I) really wanted one.\n\nBut regardless of this - AdS/CFT is, when talking about comparing\nSUGRA on AdS to N=4 SYM on the boundary, is the *low energy*\neffective theory, not a full fledged string background, right? The\nmicroscopics of the correspondence is still a string theory on both\nsides - open strings on the branes and closed strings in the bulk.\nTo really give a fully nonperturbative proof of stability, we\'d have to\nreally understand superstring theory on an AdS x S background,\n(or on the branes, including fluctuations of the branes themselves)\nand I don\'t think this has been done.\n\n> I don\'t know how to reconcile\n> this with the claim the CC might be quantized\n> appearing in hep-th/0204027, though. I don\'t think\n> anyone _knows_ a zero CC 4D "vacuum contender" to\n> be nonperturbatively stable, I suppose they\'re\n> just making educated guessing...\n\nOk - here, to reiterate my caveat from above - I\'m not\nsaying there\'s any good zero CC 4d "vacuum contender",\nbecause the zero CC 4d vacua which are "easy" are the\nones with way too much SUSY.\n\nBut maybe I\'m just being confused here - because\ntoroidally compactified type II is T-dual to living on some\nbranes, and living on some branes is just the CFT side of\nAdS/CFT, so we\'re still talking about the same "simple"\nvacua. Hmm...\n\n-Jake Mannix\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Squark <fiis5d@yahoo.com> wrote
> Well, the only really simple vacua I know are the
> 11D Minkowski space of M-theory and 5 10D string
> theories. The former probably just doesn't have
> any exciation that can possibly unstabilize it.
> The later have the dilaton, but I guess there must
> be some simple argument why it can't "go wild"
> (for type IIA it would mean decompactification
> into 11 dimensions!), I dunno.
Right, and I was thinking of the really simple
compactifications of these - like the maximal
SUSY preserving toroidal kind, or AdS x S kind.
> > > For cohomology classes with no stable
> > > vacuum we probably get decompactification.
> >
> > And if we're already fully decompactified?
>
> Why decompactified? We are compactified to 4
> dimensions, like we should be. At least _I_
> am, you never know with the internet... ;-)
Heh - I'm think we just ended up talking at angles
a litte bit - I was considering *any* possible vacuum,
not just the ones which have a M_4 x CY
decomposition, for the purposes of the argument
on "which vacuua do we know are stable/metastable".
These other vacuua (11 or 10D minkowski, or
putting those on a torus, yeilding way too much SUSY,
etc...) aren't reasonable candidates for *our* vacuum,
but they're still interesting to consider as for their
fate, and their "altitude" on the landscape, for
the purposes of seeing whether we can tunnel from
here to there from one of the CY-flux vacua.
> > *Define*, or "know how to calculate"?
>
> Define. In QFT the quantum potential is essentially
> the static part of the quantum effective action,
> whereas the later is defined to be a Legendre
> transform of the generating functional. In string
> theory there's no generating functional as far as
> anybody knows (I think), there's only the S-matrix.
Right, well I think much of the arguments I've read
have boiled down to SUGRA thinking: at tree level
in g_{string}, but allowing for higher order in \alpha'.
> > Do you know how they are known to be nonperturbatively stable?
>
> Well, for negative CC we have AdS/CFT which seems
> to imply there is a stable vacuum, since there
> is one in the CFT.
Well, as long as we believe that N=4 SYM is really even
well defined in the first place - it's not asymptotically
free, so what do you mean by a nonperturbative microscopic
definition of the theory? I'm being a little bit nitpicky here,
because I think there probably is a nice way to embed N=4
in an asymptotically free SYM such that you could have a
free microscopic definition, if you (I) really wanted one.
But regardless of this - AdS/CFT is, when talking about comparing
SUGRA on AdS to N=4 SYM on the boundary, is the *low energy*
effective theory, not a full fledged string background, right? The
microscopics of the correspondence is still a string theory on both
sides - open strings on the branes and closed strings in the bulk.
To really give a fully nonperturbative proof of stability, we'd have to
really understand superstring theory on an AdS x S background,
(or on the branes, including fluctuations of the branes themselves)
and I don't think this has been done.
> I don't know how to reconcile
> this with the claim the CC might be quantized
> appearing in http://www.arxiv.org/abs/hep-th/0204027, though. I don't think
> anyone _knows_ a zero CC 4D "vacuum contender" to
> be nonperturbatively stable, I suppose they're
> just making educated guessing...
Ok - here, to reiterate my caveat from above - I'm not
saying there's any good zero CC 4d "vacuum contender",
because the zero CC 4d vacua which are "easy" are the
ones with way too much SUSY.
But maybe I'm just being confused here - because
toroidally compactified type II is T-dual to living on some
branes, and living on some branes is just the CFT side of
AdS/CFT, so we're still talking about the same "simple"
vacua. Hmm...
-Jake Mannix
Urs Schreiber
May21-04, 09:35 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>"Jake Mannix" <jake@rset.net> schrieb im Newsbeitrag\nnews:12c1bbee.0405202019.7ba08d48-100000@posting.google.com...\n\n> Ok - here, to reiterate my caveat from above - I\'m not\n> saying there\'s any good zero CC 4d "vacuum contender",\n> because the zero CC 4d vacua which are "easy" are the\n> ones with way too much SUSY.\n\nBTW, apparently even the more elaborate ones and the ones with other values\nof the CC are so far all unlikely to not violate current observations. See\nthe nice discussion at\n\nhttp://golem.ph.utexas.edu/~distler/blog/archives/000348.html .\n\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>"Jake Mannix" <jake@rset.net> schrieb im Newsbeitrag
news:12c1bbee.0405202019.7ba08d48-100000@posting.google.com...
> Ok - here, to reiterate my caveat from above - I'm not
> saying there's any good zero CC 4d "vacuum contender",
> because the zero CC 4d vacua which are "easy" are the
> ones with way too much SUSY.
BTW, apparently even the more elaborate ones and the ones with other values
of the CC are so far all unlikely to not violate current observations. See
the nice discussion at
http://golem.ph.utexas.edu/~distler/blog/archives/000348.html .
Urs Schreiber
May21-04, 10:01 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>"Charlie Stromeyer Jr." <cstromey@hotmail.com> schrieb im Newsbeitrag\nnews:61773ed7.0405191459.23d6d8a0-100000@posting.google.com...\n\n> Here, I am only roughly paraphrasing what\n> I remember to be what Lubos wrote:\n>\n> "It would have been a large waste of time for some 19th century\n> physicists to have used Newton\'s equations in an attempt to calculate\n> the expansion of the universe instead of first waiting for the\n> necessary foundational framework, which of course was GTR."\n>\n> When I read this remark I almost slapped my own forehead :-) because\n> I interpreted this remark as a succinct expression of my own\n> intuitions at the time that some string theorists may have been overly\n> speculating about dS spacetimes, large extra dimensions, too many\n> different vacua, etc. instead of first trying to gain a better\n> understanding of what I felt would more likely be something like\n> underlying and foundational principles or concepts.\n\nIs it generally believed that one such concept deserving better\nunderstanding might be closed (super)string field theory, or is it believed\nthat this wouldn\'t help much (because, maybe, closedSFT isn\'t expected to\ncapture all non-perturbative degrees of freedom or the like)?\n\nProbably I am being too naive, but at least in the "toy" example of open\nbosonic SFT it is possible to non-perturbatively calculate the vacua of the\ntheory. So it might seem reasonable to guess that analogously closed\n(super)string field theory could help put the current search for viable and\nrealistic vacua on a sounder basis.\n\nOf course I realize that apparently very few people are working in this\ndirection. I\'d be interested in understanding if this is due to the\ndifficutlty in making progress or due to the believe that closedSFT won\'t be\nthe right tool to address these questions.\n\nAs readers of this list will have noticed, I am still very much at the\nbeginning of learning about string field theory. But in my attempt to\nunderstand its relation to deformations of worldsheet CFTs I today came\nacross a very nice old paper by Ashoke Sen:\n\nAshoke Sen:\nOn the background independence of string field theory,\nNucl.Phys.B345:551-583,1990\n(hyperlink at http://golem.ph.utexas.edu/string/index.shtml)\n\nwhich discusses this question from the point of view of background\nindependence of SFT.\n\nIn these and related papers it is claimed to be shown that open as well as\nclosed SFT are indeed background independent, in the sense that the theory\nis independent of the CFT with respect to which the BRST operator is\nconstructed and the correlators in its action are evaluated. Of course\nthat\'s just a slightly stronger statement than that of the Hata paper:\n\nHiroyuki Kata:\nPregeometrical String Field Theory: Creation of Space-Time and Motion\nhttp://golem.ph.utexas.edu/string/archives/000356.html#c000998\n\nwhich Lubos kindly pointed me to, recently.\n\nMy question is: There is considerable effort in understanding the "true\nvacuum" of bosonic open string field theory; is anyone trying to analogously\nstudy the "true vacuum" of closed string field theory (bosonic or susy)? I\nknow there is a problem with the infinity of interaction terms, but couldn\'t\none get some approximate results by an appropriate truncation? Couldn\'t that\nbe used to study the question of vacuum selection in string theory?\n\nI\'d be grateful if anyone could point me to any literature addressing this\nquestion.\n\n\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>"Charlie Stromeyer Jr." <cstromey@hotmail.com> schrieb im Newsbeitrag
news:61773ed7.0405191459.23d6d8a0-100000@posting.google.com...
> Here, I am only roughly paraphrasing what
> I remember to be what Lubos wrote:
>
> "It would have been a large waste of time for some 19th century
> physicists to have used Newton's equations in an attempt to calculate
> the expansion of the universe instead of first waiting for the
> necessary foundational framework, which of course was GTR."
>
> When I read this remark I almost slapped my own forehead :-) because
> I interpreted this remark as a succinct expression of my own
> intuitions at the time that some string theorists may have been overly
> speculating about dS spacetimes, large extra dimensions, too many
> different vacua, etc. instead of first trying to gain a better
> understanding of what I felt would more likely be something like
> underlying and foundational principles or concepts.
Is it generally believed that one such concept deserving better
understanding might be closed (super)string field theory, or is it believed
that this wouldn't help much (because, maybe, closedSFT isn't expected to
capture all non-perturbative degrees of freedom or the like)?
Probably I am being too naive, but at least in the "toy" example of open
bosonic SFT it is possible to non-perturbatively calculate the vacua of the
theory. So it might seem reasonable to guess that analogously closed
(super)string field theory could help put the current search for viable and
realistic vacua on a sounder basis.
Of course I realize that apparently very few people are working in this
direction. I'd be interested in understanding if this is due to the
difficutlty in making progress or due to the believe that closedSFT won't be
the right tool to address these questions.
As readers of this list will have noticed, I am still very much at the
beginning of learning about string field theory. But in my attempt to
understand its relation to deformations of worldsheet CFTs I today came
across a very nice old paper by Ashoke Sen:
Ashoke Sen:
On the background independence of string field theory,
Nucl.Phys.B345:551-583,1990
(hyperlink at http://golem.ph.utexas.edu/string/index.shtml)
which discusses this question from the point of view of background
independence of SFT.
In these and related papers it is claimed to be shown that open as well as
closed SFT are indeed background independent, in the sense that the theory
is independent of the CFT with respect to which the BRST operator is
constructed and the correlators in its action are evaluated. Of course
that's just a slightly stronger statement than that of the Hata paper:
Hiroyuki Kata:
Pregeometrical String Field Theory: Creation of Space-Time and Motion
http://golem.ph.utexas.edu/string/archives/000356.html#c000998
which Lubos kindly pointed me to, recently.
My question is: There is considerable effort in understanding the "true
vacuum" of bosonic open string field theory; is anyone trying to analogously
study the "true vacuum" of closed string field theory (bosonic or susy)? I
know there is a problem with the infinity of interaction terms, but couldn't
one get some approximate results by an appropriate truncation? Couldn't that
be used to study the question of vacuum selection in string theory?
I'd be grateful if anyone could point me to any literature addressing this
question.
Charlie Stromeyer Jr.
May22-04, 06:54 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Urs Schreiber <Urs.Schreiber@uni-essen.de> wrote in message news:\n\n> I\'d be grateful if anyone could point me to any literature addressing this\n> question.\n\nHere is my view on this topic of background indpendence and then I\nrecommend a new review paper which you will find useful:\n\nOne does not discard the best ideas of Newton or Einstein unless one\nhas an extremely good mathematical, theoretical or empirical reason\nfor doing so. I continue to believe that one day in the distant future\nperhaps Edward Witten may be invited by Newton and Einstein into a new\nholy trinity so that the three of them can contemplate heavenly\nmechanics :-)\n\nIn the autumn of 1997, I told Juan Maldacena that I suspected that\nsome of his then current thinking about black holes was not sufficient\nand that he should try to think more about the implications due to\nthe need for background independence.\n\nI didn\'t know anything at the time about loop quantum gravity and so\nmy view was that string theory should be fundamental and that\ntheorists should try to figure out more about how to include quantum\ngravity into string theory. In this case, the background geometry\ncould not exist a priori but would instead emerge from a very\nnon-perturbative effect which is the condensation of strings.\n\nI had gotten this view from reading page one of [1] which made me more\naware of the importance of a paper by Witten from almost a decade\nprior which is his TQFT paper in CMP 117 (1988) 353. I also felt that,\nsimilarly with the case of Newton and Einstein, theorists should have\nbeen paying more attention to what seemed to me and some others to be\nperhaps the best insights from Witten.\n\nHowever, it is important for me to admit that I never found (circa\n1997-8) any major or fatal flaws with Maldacena\'s fundamental ideas,\nand this is just one of various important reasons why I continue to\nbelieve that Maldacena may also be a genius, although whether we\ncurrently believe that individuals such as Witten, Vafa, Strominger,\nMaldacena etc. are geniuses does not truly matter because only time\nwill tell.\n\nBack to the issue of condensation, you may want to look at this paper\ncalled "Closed String Tachyon Condensation: An Overview" [2].\n\nAlso, the answer to your question about the noncommutative butterfly\npaper is yes. We might even think of their ansatz as like a "cocoon"\nbecause it can yield the string solutions, but just make sure not to\nconfuse any caterpillars with those worms who may be wearing sweaters\n:-)\n\n\n[1] http://arxiv.org/abs/hep-th/9708039\n\n[2] http://arxiv.org/abs/hep-th/0405064\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Urs Schreiber <Urs.Schreiber@uni-essen.de> wrote in message news:
> I'd be grateful if anyone could point me to any literature addressing this
> question.
Here is my view on this topic of background indpendence and then I
recommend a new review paper which you will find useful:
One does not discard the best ideas of Newton or Einstein unless one
has an extremely good mathematical, theoretical or empirical reason
for doing so. I continue to believe that one day in the distant future
perhaps Edward Witten may be invited by Newton and Einstein into a new
holy trinity so that the three of them can contemplate heavenly
mechanics :-)
In the autumn of 1997, I told Juan Maldacena that I suspected that
some of his then current thinking about black holes was not sufficient
and that he should try to think more about the implications due to
the need for background independence.
I didn't know anything at the time about loop quantum gravity and so
my view was that string theory should be fundamental and that
theorists should try to figure out more about how to include quantum
gravity into string theory. In this case, the background geometry
could not exist a priori but would instead emerge from a very
non-perturbative effect which is the condensation of strings.
I had gotten this view from reading page one of [1] which made me more
aware of the importance of a paper by Witten from almost a decade
prior which is his TQFT paper in CMP 117 (1988) 353. I also felt that,
similarly with the case of Newton and Einstein, theorists should have
been paying more attention to what seemed to me and some others to be
perhaps the best insights from Witten.
However, it is important for me to admit that I never found (circa
1997-8) any major or fatal flaws with Maldacena's fundamental ideas,
and this is just one of various important reasons why I continue to
believe that Maldacena may also be a genius, although whether we
currently believe that individuals such as Witten, Vafa, Strominger,
Maldacena etc. are geniuses does not truly matter because only time
will tell.
Back to the issue of condensation, you may want to look at this paper
called "Closed String Tachyon Condensation: An Overview" [2].
Also, the answer to your question about the noncommutative butterfly
paper is yes. We might even think of their ansatz as like a "cocoon"
because it can yield the string solutions, but just make sure not to
confuse any caterpillars with those worms who may be wearing sweaters
:-)
[1] http://arxiv.org/abs/http://www.arxiv.org/abs/hep-th/9708039
[2] http://arxiv.org/abs/http://www.arxiv.org/abs/hep-th/0405064
Urs Schreiber
May22-04, 07:39 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>On Sat, 22 May 2004, Charlie Stromeyer Jr. wrote:\n\n> Back to the issue of condensation, you may want to look at this paper\n> called "Closed String Tachyon Condensation: An Overview" [2].\n\nMany thanks for the reference. So apparently the bosonic closed string\ntachyon condensation is being studied, but it is not clear yet what\nthe resulting "true vacuum" really is, e.g. whether fermions appear\nsomehow, as has been speculated, and if the superstring ppears.\n\nBTW, can we have closed superstring tachyons? Open superstring\ntachyons appear in unstable configurations of brane/antibrane pairs,\nbut do we also get closed superstring tachyons this way?\n\nRecently there was an interesting paper related to closed\nsuperstring fielrd theory:\n\nP. Grassi & L. Tamassia\nVertex Operators for Closed Superstrings\nhep-th/0405072\n\nUnfortunately some other tasks currently prevent me from\nreading this in detail, but apparently in there deformations\nof the BRST operator are discussed (equation 2.12) which,\namong other things, apparently describe _constant_ RR\nbackground fields. (compare item b in the outlook on p. 32).\n\nMaybe I am hallucinating, but this might be the answer to\nthe little problem that I addressed at\n\n\nString Coffee Table: Simple but not trivial\nhttp://golem.ph.utexas.edu/string/archives/000323.html\n\nwhere I asked if it might make sense to study the BRST\noperator deformations with RR vertices discussed by\nGiannakis in the relatively simple case of constant RR\nbackgrounds, that have for instance be discussed recently\nin hep-th/0402160 .\n\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>On Sat, 22 May 2004, Charlie Stromeyer Jr. wrote:
> Back to the issue of condensation, you may want to look at this paper
> called "Closed String Tachyon Condensation: An Overview" [2].
Many thanks for the reference. So apparently the bosonic closed string
tachyon condensation is being studied, but it is not clear yet what
the resulting "true vacuum" really is, e.g. whether fermions appear
somehow, as has been speculated, and if the superstring ppears.
BTW, can we have closed superstring tachyons? Open superstring
tachyons appear in unstable configurations of brane/antibrane pairs,
but do we also get closed superstring tachyons this way?
Recently there was an interesting paper related to closed
superstring fielrd theory:
P. Grassi & L. Tamassia
Vertex Operators for Closed Superstrings
http://www.arxiv.org/abs/hep-th/0405072
Unfortunately some other tasks currently prevent me from
reading this in detail, but apparently in there deformations
of the BRST operator are discussed (equation 2.12) which,
among other things, apparently describe _constant_ RR
background fields. (compare item b in the outlook on p. 32).
Maybe I am hallucinating, but this might be the answer to
the little problem that I addressed at
String Coffee Table: Simple but not trivial
http://golem.ph.utexas.edu/string/archives/000323.html
where I asked if it might make sense to study the BRST
operator deformations with RR vertices discussed by
Giannakis in the relatively simple case of constant RR
backgrounds, that have for instance be discussed recently
in http://www.arxiv.org/abs/hep-th/0402160 .
Urs Schreiber
May22-04, 02:56 PM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>On Sat, 22 May 2004, Urs Schreiber wrote:\n\n> P. Grassi & L. Tamassia\n> Vertex Operators for Closed Superstrings\n> hep-th/0405072\n\nThis relies on "pure spinor formalism" where the BRST\noperator for the superstring has the nice concise form\n\nQ = \\oint \\lambda^\\alpha p_\\alpha\n\nwhere p_\\alpha is the target space susy generator and\n\\lambda^\\alpha an associated (bosonic) ghost which is\n"pure spinor" meaning that\n\n\\lambda \\gamma_m \\lambda = 0\n\n\nbecause that obviously ensures nilpotency of th above Q,\nsince p_\\alpha, being the susy generator, squares to\nsomething proportional to \\gamma^m_{\\alpha\\beta}.\n\n\nThis formalism is discussed in\n\nNathan Berkovits & Paul Howe:\nTen-Dimensional Supergravity Constraints form the Pure Spinor Formalism\nfor the Superstring\nhep-th/0112160 .\n\nFine. What I don\'t see yet is how precisely this is related\nto the usual RNS and/or GS formalism. Can the pure spinor\nformalism be derived somehow from either one o of these?\nCan one for instance re-express the pure spinor ghosts\nin terms of the usual reparemeterization super ghosts?\n\n\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>On Sat, 22 May 2004, Urs Schreiber wrote:
> P. Grassi & L. Tamassia
> Vertex Operators for Closed Superstrings
> http://www.arxiv.org/abs/hep-th/0405072
This relies on "pure spinor formalism" where the BRST
operator for the superstring has the nice concise form
Q = \oint \lambda^\alpha p_\alpha
where p_\alpha is the target space susy generator and
\lambda^\alpha an associated (bosonic) ghost which is
"pure spinor" meaning that
\lambda \gamma_m \lambda =
because that obviously ensures nilpotency of th above Q,
since p_\alpha, being the susy generator, squares to
something proportional to \gamma^m_{\alpha\beta}.
This formalism is discussed in
Nathan Berkovits & Paul Howe:
Ten-Dimensional Supergravity Constraints form the Pure Spinor Formalism
for the Superstring
http://www.arxiv.org/abs/hep-th/0112160 .
Fine. What I don't see yet is how precisely this is related
to the usual RNS and/or GS formalism. Can the pure spinor
formalism be derived somehow from either one o of these?
Can one for instance re-express the pure spinor ghosts
in terms of the usual reparemeterization super ghosts?
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Hey everyone.\n\nFirst of all, I\'ve read Lenny Susskind\'s paper\n"The Anthropic Landscape of String Theory" (hep-th/0302219)\nand understood far better the whole idea of the "landscape".\nI\'d like to summarize the things I\'ve been missing before.\n\n1) If I\'m not missing anything (this time), the quantum\npotential _is_ the cosmological constant. This is almost\na trivial observation: both correspond to the energy density\nof the vacuum. At least this is so at minima of the quantum\npotential, i.e. at (possibly false) vacua: I\'m not sure the\nstatement makes sense elsewhere.\n\n2) It is currently believed a transition from a universe\nwith non-negative cosmological constant to a negative\ncosmological constant one is impossible. Apparently this is\nso because classical gravity considerations imply the\nresulting universe is a big crunch universe and it is not\nclear whether the later makes sense in string theory.\nFrankly, this whole idea is not clear to me since we\'re\nliving in a big bang universe, and if that makes sense, why\nnot big crunch? Possible there are additional arguments\nagainst this kind of transitions which I am unaware of.\n\n3) A SUSY vacuum with no cosmological constant term in the\ncorresponding low energy effective classical action is\nneccesarily stable since the vacuum energy vanishes as a\nresult of SUSY and transitions to negative vacuum energy\nare forbidden.\n\n4) The later vacua form a continuous space, the so called\n"supermoduli" space. Calabi-Yau compactifications with no\nfluxes/wrapped branes are included, as far as I understand.\n\n5) The "landscape" consists of metastable vacua with\nvarious non-negative values of the cosmological constant.\nThe primary example is adding 7-form field stength flux\non the M-theory level. Four of the flux\'s indices are\nchosen to be the non-compactified dimensions. The result\nis a constant energy density in spacetime i.e.\ncosmological constant. This flux changes by quantized\namounts since the brane charges are quantized. The vacuum\ndecays via the formation of a brane the space enclosed by\nwhich carries no (or less) flux (since the brane is\ncharged). The potential barrier results, as far as I\nunderstand, from the fact brane tension goes as r^2\nwhereas the energy associated to the flux as r^3 (so for\ntoo small r the brane tension is bigger). Such metastable\nvacua decay until they hit the supermoduli space.\nSusskind attempt to analyze this process via classical\ngravity consideration, but he himself admits certain\nflaws in this analysis.\n\nJake Mannix <jake@rset.net> wrote in message news:<12c1bbee.0405202019.7ba08d48-100000@posting.google.com>...\n> > > And if we\'re already fully decompactified?\n> >\n> > Why decompactified? We are compactified to 4\n> > dimensions, like we should be. At least _I_\n> > am, you never know with the internet... ;-)\n>\n> Heh - I\'m think we just ended up talking at angles\n> a litte bit - I was considering *any* possible vacuum,\n> not just the ones which have a M_4 x CY\n> decomposition, for the purposes of the argument\n> on "which vacuua do we know are stable/metastable".\n\nSorry, I was misreading you: I thought you said "aren\'t\nwe already fully decompactified".\n\n> Right, well I think much of the arguments I\'ve read\n> have boiled down to SUGRA thinking: at tree level\n> in g_string, but allowing for higher order in \\alpha\'.\n\nIsn\'t SUGRA thinking tree level both in g and alpha\'?\nHigher order in alpha\' yields tree level string theory.\nIn fact, SUGRA includes some g-nonperturbative effects,\nwhich is analogous to instants in QFT that are\nnonperturbative but exist already on the classical\nlevel.\n\n> Well, as long as we believe that N=4 SYM is really even\n> well defined in the first place - it\'s not asymptotically\n> free, so what do you mean by a nonperturbative microscopic\n> definition of the theory?\n\nI don\'t know much about SYM but you might be right, this is\na subtlety.\n\n> But regardless of this - AdS/CFT is, when talking about comparing\n> SUGRA on AdS to N=4 SYM on the boundary, is the *low energy*\n> effective theory, not a full fledged string background, right?\n\nNo, not at all. The dual CFT should yield a complete\nnonperturbative description of string theory in AdS.\nOr am I misunderstanding what you\'re saying here?\n\nBest regards,\nSquark.\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Hey everyone.
First of all, I've read Lenny Susskind's paper
"The Anthropic Landscape of String Theory" (http://www.arxiv.org/abs/hep-th/0302219)
and understood far better the whole idea of the "landscape".
I'd like to summarize the things I've been missing before.
1) If I'm not missing anything (this time), the quantum
potential _is_ the cosmological constant. This is almost
a trivial observation: both correspond to the energy density
of the vacuum. At least this is so at minima of the quantum
potential, i.e. at (possibly false) vacua: I'm not sure the
statement makes sense elsewhere.
2) It is currently believed a transition from a universe
with non-negative cosmological constant to a negative
cosmological constant one is impossible. Apparently this is
so because classical gravity considerations imply the
resulting universe is a big crunch universe and it is not
clear whether the later makes sense in string theory.
Frankly, this whole idea is not clear to me since we're
living in a big bang universe, and if that makes sense, why
not big crunch? Possible there are additional arguments
against this kind of transitions which I am unaware of.
3) A SUSY vacuum with no cosmological constant term in the
corresponding low energy effective classical action is
neccesarily stable since the vacuum energy vanishes as a
result of SUSY and transitions to negative vacuum energy
are forbidden.
4) The later vacua form a continuous space, the so called
"supermoduli" space. Calabi-Yau compactifications with no
fluxes/wrapped branes are included, as far as I understand.
5) The "landscape" consists of metastable vacua with
various non-negative values of the cosmological constant.
The primary example is adding 7-form field stength flux
on the M-theory level. Four of the flux's indices are
chosen to be the non-compactified dimensions. The result
is a constant energy density in spacetime i.e.
cosmological constant. This flux changes by quantized
amounts since the brane charges are quantized. The vacuum
decays via the formation of a brane the space enclosed by
which carries no (or less) flux (since the brane is
charged). The potential barrier results, as far as I
understand, from the fact brane tension goes as r^2
whereas the energy associated to the flux as r^3 (so for
too small r the brane tension is bigger). Such metastable
vacua decay until they hit the supermoduli space.
Susskind attempt to analyze this process via classical
gravity consideration, but he himself admits certain
flaws in this analysis.
Jake Mannix <jake@rset.net> wrote in message news:<12c1bbee.0405202019.7ba08d48-100000@posting.google.com>...
> > > And if we're already fully decompactified?
> >
> > Why decompactified? We are compactified to 4
> > dimensions, like we should be. At least _I_
> > am, you never know with the internet... ;-)
>
> Heh - I'm think we just ended up talking at angles
> a litte bit - I was considering *any* possible vacuum,
> not just the ones which have a M_4 x CY
> decomposition, for the purposes of the argument
> on "which vacuua do we know are stable/metastable".
Sorry, I was misreading you: I thought you said "aren't
we already fully decompactified".
> Right, well I think much of the arguments I've read
> have boiled down to SUGRA thinking: at tree level
> in g_{string}, but allowing for higher order in \alpha'.
Isn't SUGRA thinking tree level both in g and \alpha'?
Higher order in \alpha' yields tree level string theory.
In fact, SUGRA includes some g-nonperturbative effects,
which is analogous to instants in QFT that are
nonperturbative but exist already on the classical
level.
> Well, as long as we believe that N=4 SYM is really even
> well defined in the first place - it's not asymptotically
> free, so what do you mean by a nonperturbative microscopic
> definition of the theory?
I don't know much about SYM but you might be right, this is
a subtlety.
> But regardless of this - AdS/CFT is, when talking about comparing
> SUGRA on AdS to N=4 SYM on the boundary, is the *low energy*
> effective theory, not a full fledged string background, right?
No, not at all. The dual CFT should yield a complete
nonperturbative description of string theory in AdS.
Or am I misunderstanding what you're saying here?
Best regards,
Squark.
Urs Schreiber
May24-04, 03:14 PM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>"Squark" <fiis5d@yahoo.com> schrieb im Newsbeitrag\nnews:939044f.0405231017.41f7dde9-100000@posting.google.com...\n> Hey everyone.\n>\n> First of all, I\'ve read Lenny Susskind\'s paper\n> "The Anthropic Landscape of String Theory" (hep-th/0302219)\n> and understood far better the whole idea of the "landscape".\n\nI haven\'t become much more familiar with this landscaping since we briefly\ntalked about this paper on sci.physics.research some time ago:\n\nhttp://groups.google.de/groups?selm=206f2305.0303080825.2401289d%40posting .google.com\n\nand when re-reading it I can\'t help but feel that this entire discussion is\npremature, since apparently way too litle is known about the mechanisms\nunder discussion.\n\n> Susskind attempt to analyze this process via classical\n> gravity consideration, but he himself admits certain\n> flaws in this analysis.\n\nIn particular I am confused about the last sentence on p. 9, where it says:\n\n"However in a gravitational theory in which space is bounded (as in the\nstatic patch) the total energy is always zero, at least classically." (pp.\n9-10 of hep-th/0302219)\n\nI don\'t know what this is supposed to mean. It even seems to contradict the\nfact that the discussion is precisely about the non-vanishing energy content\nof the universe.\n\n(Maybe for the sake of argument it would suffice at this point to argue that\nthe Boltzmann supression factor is negligible compared to the entropy\nsupression factor?)\n\nTo me, the most interesting aspect of the excitement generated by the KKLT\npaper seems to be that it indicates that when indeed non-perturbative\neffects are taken into account, _most_ of the moduli do get stabilized.\nModuli stabilization has been one of the big problems of string theory as\nsuch in the past, and it is nice to see that apparently the\nnon-perturbatibve theory is gonna fix it - at least to my simple mind.\n\nOn\n\nhttp://golem.ph.utexas.edu/~distler/blog/archives/000359.html#c001036\n\nSavdeep Sethi writes\n\n"there are no examples of compactifications with all moduli stabilized at\nlarge volume. No-one has come even remotely close. That is the burden to be\nmet by anyone claiming to have a construction." (S. Sethi)\n\nOn the other hand, people seem to disagree how close is close:\n\nJacques Distler writes on\n\nhttp://golem.ph.utexas.edu/~distler/blog/archives/000359.html#c001037 :\n\n"I would call the Rutgers paper "remotely close."" (J. Distler)\n\nMy impression is that the total landscape discussion might be much more\nintersting in a couple of years, when the general mechanism are better\nunderstood and one can actually talk about specific results. But I may be\nwrong, of course.\n\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>"Squark" <fiis5d@yahoo.com> schrieb im Newsbeitrag
news:939044f.0405231017.41f7dde9-100000@posting.google.com...
> Hey everyone.
>
> First of all, I've read Lenny Susskind's paper
> "The Anthropic Landscape of String Theory" (http://www.arxiv.org/abs/hep-th/0302219)
> and understood far better the whole idea of the "landscape".
I haven't become much more familiar with this landscaping since we briefly
talked about this paper on sci.physics.research some time ago:
http://groups.google.de/groups?selm=206f2305.0303080825.2401289d%40posting .google.com
and when re-reading it I can't help but feel that this entire discussion is
premature, since apparently way too litle is known about the mechanisms
under discussion.
> Susskind attempt to analyze this process via classical
> gravity consideration, but he himself admits certain
> flaws in this analysis.
In particular I am confused about the last sentence on p. 9, where it says:
"However in a gravitational theory in which space is bounded (as in the
static patch) the total energy is always zero, at least classically." (pp.
9-10 of http://www.arxiv.org/abs/hep-th/0302219)
I don't know what this is supposed to mean. It even seems to contradict the
fact that the discussion is precisely about the non-vanishing energy content
of the universe.
(Maybe for the sake of argument it would suffice at this point to argue that
the Boltzmann supression factor is negligible compared to the entropy
supression factor?)
To me, the most interesting aspect of the excitement generated by the KKLT
paper seems to be that it indicates that when indeed non-perturbative
effects are taken into account, _most_ of the moduli do get stabilized.
Moduli stabilization has been one of the big problems of string theory as
such in the past, and it is nice to see that apparently the
non-perturbatibve theory is gonna fix it - at least to my simple mind.
On
http://golem.ph.utexas.edu/~distler/blog/archives/000359.html#c001036
Savdeep Sethi writes
"there are no examples of compactifications with all moduli stabilized at
large volume. No-one has come even remotely close. That is the burden to be
met by anyone claiming to have a construction." (S. Sethi)
On the other hand, people seem to disagree how close is close:
Jacques Distler writes on
http://golem.ph.utexas.edu/~distler/blog/archives/000359.html#c001037 :
"I would call the Rutgers paper "remotely close."" (J. Distler)
My impression is that the total landscape discussion might be much more
intersting in a couple of years, when the general mechanism are better
understood and one can actually talk about specific results. But I may be
wrong, of course.
Charlie Stromeyer Jr.
May25-04, 04:15 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Urs Schreiber <Urs.Schreiber@uni-essen.de> wrote in message news:\n>\n> > P. Grassi & L. Tamassia\n> > Vertex Operators for Closed Superstrings\n> > hep-th/0405072\n\nHi Urs, the only important work I must get done over the next few\nweeks is with advising an MIT engineer about math and economics. This\nmeans that I will have some time to think about your questions.\n\nFor a newsgroup named "sci.physics.strings" there seems to be few\nstring theorists posting here. Perhaps you might want to consider\nemailing the string theory community to let them know about this\nnewsgroup, or have you already scared them away as they run for cover\nfrom all the flying intellectual bullets that are your questions ?-)\n\n> Fine. What I don\'t see yet is how precisely this is related\n> to the usual RNS and/or GS formalism. Can the pure spinor\n> formalism be derived somehow from either one o of these?\n\nYes, and for more clarification also see the earlier paper\n(hep-th/0405007).\n\n> Can one for instance re-express the pure spinor ghosts\n> in terms of the usual reparemeterization super ghosts?\n\nI am not sure I understand what you are asking. In the Berkovits\napproach there are pure spinors as ghosts but there are no worldsheet\n(super)diffeomorphism ghosts.\n\nYou may also want to look at some of the techniques that have been\nused for Type 0 strings because these strings are described by N=1\nsusy worldsheet theories (hep-th/0308123 and 0309028).\n\n\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Urs Schreiber <Urs.Schreiber@uni-essen.de> wrote in message news:
>
> > P. Grassi & L. Tamassia
> > Vertex Operators for Closed Superstrings
> > http://www.arxiv.org/abs/hep-th/0405072
Hi Urs, the only important work I must get done over the next few
weeks is with advising an MIT engineer about math and economics. This
means that I will have some time to think about your questions.
For a newsgroup named "sci.physics.strings" there seems to be few
string theorists posting here. Perhaps you might want to consider
emailing the string theory community to let them know about this
newsgroup, or have you already scared them away as they run for cover
from all the flying intellectual bullets that are your questions ?-)
> Fine. What I don't see yet is how precisely this is related
> to the usual RNS and/or GS formalism. Can the pure spinor
> formalism be derived somehow from either one o of these?
Yes, and for more clarification also see the earlier paper
(http://www.arxiv.org/abs/hep-th/0405007).
> Can one for instance re-express the pure spinor ghosts
> in terms of the usual reparemeterization super ghosts?
I am not sure I understand what you are asking. In the Berkovits
approach there are pure spinors as ghosts but there are no worldsheet
(super)diffeomorphism ghosts.
You may also want to look at some of the techniques that have been
used for Type strings because these strings are described by N=1
susy worldsheet theories (http://www.arxiv.org/abs/hep-th/0308123 and 0309028).
Urs Schreiber
May25-04, 02:30 PM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>On Tue, 25 May 2004, Charlie Stromeyer Jr. wrote:\n\n> Urs Schreiber <Urs.Schreiber@uni-essen.de> wrote in message news:\n\n> > Fine. What I don\'t see yet is how precisely this is related\n> > to the usual RNS and/or GS formalism. Can the pure spinor\n> > formalism be derived somehow from either one o of these?\n>\n> Yes, and for more clarification also see the earlier paper\n> (hep-th/0405007).\n\nAh, thanks. I haven\'t gone through the details (a science of its own, it\nseems), but the introduction of that paper certainly helps. Interestingly,\nthe authors there do _not_ use the pure spinor condition but instead\nitroduce another BRST operator to enforce the corresponding conditions.\n\nI haven\'t figured out if this is anyhow\nrelated to the appearance of the second BRST-like operator in the WZW-like\nsuperstring field theory by Berkovits (where Q_2 ~ eta), but probably it\nis.\n\n>\n> > Can one for instance re-express the pure spinor ghosts\n> > in terms of the usual reparemeterization super ghosts?\n>\n> I am not sure I understand what you are asking.\n\nI was thinking that maybe the lambda are combinations of the rep\nsuperghosts. But apparently that\'s the wrong line of thinking.\n\n> In the Berkovits\n> approach there are pure spinors as ghosts but there are no worldsheet\n> (super)diffeomorphism ghosts.\n\nHm. In section 5 the authors of the above paper do discuss worldsheet\ndiffeos and the super diffeo ghosts it seems.\n\n> You may also want to look at some of the techniques that have been\n> used for Type 0 strings because these strings are described by N=1\n> susy worldsheet theories (hep-th/0308123 and 0309028).\n\nLater. Maybe when I find a method to increase the number of hours in one\nday ;-)\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>On Tue, 25 May 2004, Charlie Stromeyer Jr. wrote:
> Urs Schreiber <Urs.Schreiber@uni-essen.de> wrote in message news:
> > Fine. What I don't see yet is how precisely this is related
> > to the usual RNS and/or GS formalism. Can the pure spinor
> > formalism be derived somehow from either one o of these?
>
> Yes, and for more clarification also see the earlier paper
> (http://www.arxiv.org/abs/hep-th/0405007).
Ah, thanks. I haven't gone through the details (a science of its own, it
seems), but the introduction of that paper certainly helps. Interestingly,
the authors there do _not_ use the pure spinor condition but instead
itroduce another BRST operator to enforce the corresponding conditions.
I haven't figured out if this is anyhow
related to the appearance of the second BRST-like operator in the WZW-like
superstring field theory by Berkovits (where Q_2 ~ \eta), but probably it
is.
>
> > Can one for instance re-express the pure spinor ghosts
> > in terms of the usual reparemeterization super ghosts?
>
> I am not sure I understand what you are asking.
I was thinking that maybe the \lambda are combinations of the rep
superghosts. But apparently that's the wrong line of thinking.
> In the Berkovits
> approach there are pure spinors as ghosts but there are no worldsheet
> (super)diffeomorphism ghosts.
Hm. In section 5 the authors of the above paper do discuss worldsheet
diffeos and the super diffeo ghosts it seems.
> You may also want to look at some of the techniques that have been
> used for Type strings because these strings are described by N=1
> susy worldsheet theories (http://www.arxiv.org/abs/hep-th/0308123 and 0309028).
Later. Maybe when I find a method to increase the number of hours in one
day ;-)
Charlie Stromeyer Jr.
May26-04, 02:15 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Urs Schreiber <Urs.Schreiber@uni-essen.de> wrote in message news:\n\n> > Yes, and for more clarification also see the earlier paper\n> > (hep-th/0405007).\n>\n> Ah, thanks. I haven\'t gone through the details (a science of its own, it\n> seems)\n\nIs it still a science when you find either the Devil or God in the\ndetails ?-)\n\n> > In the Berkovits\n> > approach there are pure spinors as ghosts but there are no worldsheet\n> > (super)diffeomorphism ghosts.\n>\n> Hm. In section 5 the authors of the above paper do discuss worldsheet\n> diffeos and the super diffeo ghosts it seems.\n\nCorrect, but as you have already seen this paper is not strictly the\noriginal Berkovits\' approach but a modification of it. This same paper\nalso refers to another modification of the Berkovits\' approach which\nis a generalization called the EPS formailism (hep-th/0404141), but\ndon\'t worry because the "B-ghosts" here are less scary than "Super\nGhosts" :-)\n\n> > You may also want to look at some of the techniques that have been\n> > used for Type 0 strings because these strings are described by N=1\n> > susy worldsheet theories (hep-th/0308123 and 0309028).\n>\n> Later. Maybe when I find a method to increase the number of hours in one\n> day ;-)\n\nHave you considered GTR, or trying to capture your own mind as a known\nquantum state so that it cane be cloned? Otherwise, you will have to\nsettle for a more approximate method of cloning :-)\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Urs Schreiber <Urs.Schreiber@uni-essen.de> wrote in message news:
> > Yes, and for more clarification also see the earlier paper
> > (http://www.arxiv.org/abs/hep-th/0405007).
>
> Ah, thanks. I haven't gone through the details (a science of its own, it
> seems)
Is it still a science when you find either the Devil or God in the
details ?-)
> > In the Berkovits
> > approach there are pure spinors as ghosts but there are no worldsheet
> > (super)diffeomorphism ghosts.
>
> Hm. In section 5 the authors of the above paper do discuss worldsheet
> diffeos and the super diffeo ghosts it seems.
Correct, but as you have already seen this paper is not strictly the
original Berkovits' approach but a modification of it. This same paper
also refers to another modification of the Berkovits' approach which
is a generalization called the EPS formailism (http://www.arxiv.org/abs/hep-th/0404141), but
don't worry because the "B-ghosts" here are less scary than "Super
Ghosts" :-)
> > You may also want to look at some of the techniques that have been
> > used for Type strings because these strings are described by N=1
> > susy worldsheet theories (http://www.arxiv.org/abs/hep-th/0308123 and 0309028).
>
> Later. Maybe when I find a method to increase the number of hours in one
> day ;-)
Have you considered GTR, or trying to capture your own mind as a known
quantum state so that it cane be cloned? Otherwise, you will have to
settle for a more approximate method of cloning :-)
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Urs Schreiber <Urs.Schreiber@uni-essen.de> wrote in message news:<2hevr3Fcalc0U1-100000@uni-berlin.de>...\n> In particular I am confused about the last sentence on p. 9, where it says:\n>\n> "However in a gravitational theory in which space is bounded (as in the\n> static patch) the total energy is always zero, at least classically." (pp.\n> 9-10 of hep-th/0302219)\n>\n> I don\'t know what this is supposed to mean. It even seems to contradict the\n> fact that the discussion is precisely about the non-vanishing energy content\n> of the universe.\n\nI think that the "total energy" in this case is the Hamiltonian,\nwhich is "matter energy" + "gravitational energy" which is zero\nunless space has some asymptotic regions. Here, both of terms\nare not really well defined (in a coordinate independent fashion),\nhowever, the sum _is_. Another thing that is defined is the\n(matter) energy-momentum tensor, which is exactly the\n"non-vanishing energy content" you are talking about. It is the\nHamiltonian, though, which is the relevant quantity for\nthermodynamical considerations.\n\n> To me, the most interesting aspect of the excitement generated by the KKLT\n> paper seems to be that it indicates that when indeed non-perturbative\n> effects are taken into account, _most_ of the moduli do get stabilized.\n\nWhat is the KKLT paper, and how do most of the moduli get stabilized?\n\nBest regards,\nSquark.\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Urs Schreiber <Urs.Schreiber@uni-essen.de> wrote in message news:<2hevr3Fcalc0U1-100000@uni-berlin.de>...
> In particular I am confused about the last sentence on p. 9, where it says:
>
> "However in a gravitational theory in which space is bounded (as in the
> static patch) the total energy is always zero, at least classically." (pp.
> 9-10 of http://www.arxiv.org/abs/hep-th/0302219)
>
> I don't know what this is supposed to mean. It even seems to contradict the
> fact that the discussion is precisely about the non-vanishing energy content
> of the universe.
I think that the "total energy" in this case is the Hamiltonian,
which is "matter energy" + "gravitational energy" which is zero
unless space has some asymptotic regions. Here, both of terms
are not really well defined (in a coordinate independent fashion),
however, the sum _is_. Another thing that is defined is the
(matter) energy-momentum tensor, which is exactly the
"non-vanishing energy content" you are talking about. It is the
Hamiltonian, though, which is the relevant quantity for
thermodynamical considerations.
> To me, the most interesting aspect of the excitement generated by the KKLT
> paper seems to be that it indicates that when indeed non-perturbative
> effects are taken into account, _most_ of the moduli do get stabilized.
What is the KKLT paper, and how do most of the moduli get stabilized?
Best regards,
Squark.
Urs Schreiber
May26-04, 10:43 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>On Wed, 26 May 2004, Squark wrote:\n\n> Urs Schreiber <Urs.Schreiber@uni-essen.de> wrote in message news:<2hevr3Fcalc0U1-100000@uni-berlin.de>...\n> > In particular I am confused about the last sentence on p. 9, where it says:\n> >\n> > "However in a gravitational theory in which space is bounded (as in the\n> > static patch) the total energy is always zero, at least classically." (pp.\n> > 9-10 of hep-th/0302219)\n> >\n> > I don\'t know what this is supposed to mean. It even seems to contradict the\n> > fact that the discussion is precisely about the non-vanishing energy content\n> > of the universe.\n>\n> I think that the "total energy" in this case is the Hamiltonian,\n> which is "matter energy" + "gravitational energy" which is zero\n> unless space has some asymptotic regions.\n\nYes, after posting that message I had this idea, too, that the autor is\nprobably thinking of the fact that the _Hamiltomnian constraint_ vanishes.\nThat\'s why he says "at least classically", being aware of the well\nunderstood case of 1+1 dimensions where the Hamiltonian constraint (L0 +\n\\bar L_0) is "0" only up a quantum shift.\n\nBut if that\'s what the author is thinking of in that paragraph it really\nmakes me feel uneasy, because, as you indicated\n\n1) the fact that the Hamiltonian constraint vanishes says little about the\nenergy content of the universe (much like (L_0-1)|psi>=0 alone tells me\nnothing about the mass of a string state psi)\n\n2) the statement does not have anything to do with the figure that\naccompanies it and the conclusions drawn from it (please anyone correct\nme if I am wrong about this!)\n\n> (matter) energy-momentum tensor, which is exactly the\n> "non-vanishing energy content" you are talking about. It is the\n> Hamiltonian, though, which is the relevant quantity for\n> thermodynamical considerations.\n\nYes, that\'s what I would think. And this Hamiltonian does not vanish.\n\n> > To me, the most interesting aspect of the excitement generated by the KKLT\n> > paper seems to be that it indicates that when indeed non-perturbative\n> > effects are taken into account, _most_ of the moduli do get stabilized.\n>\n> What is the KKLT paper, and how do most of the moduli get stabilized?\n\nIt\'s\n\nKachru & Kallosh & Linde & Trivedi:\nde Sitter vacua in string theory\nhep-th/0301240\n\nwhich started most of the landscape discussion, as far as I am aware. For\na nice summary of some of the effects discussed in there see J. Distler\'s\n\n"Digging up the landscape"\nhttp://golem.ph.utexas.edu/~distler/blog/archives/000359.html\n\nand\n\n"The discretium"\nhttp://golem.ph.utexas.edu/~distler/blog/archives/000348.html.\n\nAlso see the sci.physics.strings archive for the thread\n\n"Conceptual question"\n\nwhere Shamit Kachru himself, together with J. Polchinski and W. Lerche, L.\nMotl and A. Rajaraman discuss this issue.\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>On Wed, 26 May 2004, Squark wrote:
> Urs Schreiber <Urs.Schreiber@uni-essen.de> wrote in message news:<2hevr3Fcalc0U1-100000@uni-berlin.de>...
> > In particular I am confused about the last sentence on p. 9, where it says:
> >
> > "However in a gravitational theory in which space is bounded (as in the
> > static patch) the total energy is always zero, at least classically." (pp.
> > 9-10 of http://www.arxiv.org/abs/hep-th/0302219)
> >
> > I don't know what this is supposed to mean. It even seems to contradict the
> > fact that the discussion is precisely about the non-vanishing energy content
> > of the universe.
>
> I think that the "total energy" in this case is the Hamiltonian,
> which is "matter energy" + "gravitational energy" which is zero
> unless space has some asymptotic regions.
Yes, after posting that message I had this idea, too, that the autor is
probably thinking of the fact that the _Hamiltomnian constraint_ vanishes.
That's why he says "at least classically", being aware of the well
understood case of 1+1 dimensions where the Hamiltonian constraint (L0 +
\bar L_0) is "" only up a quantum shift.
But if that's what the author is thinking of in that paragraph it really
makes me feel uneasy, because, as you indicated
1) the fact that the Hamiltonian constraint vanishes says little about the
energy content of the universe (much like (L_0-1)|\psi>=0 alone tells me
nothing about the mass of a string state \psi)
2) the statement does not have anything to do with the figure that
accompanies it and the conclusions drawn from it (please anyone correct
me if I am wrong about this!)
> (matter) energy-momentum tensor, which is exactly the
> "non-vanishing energy content" you are talking about. It is the
> Hamiltonian, though, which is the relevant quantity for
> thermodynamical considerations.
Yes, that's what I would think. And this Hamiltonian does not vanish.
> > To me, the most interesting aspect of the excitement generated by the KKLT
> > paper seems to be that it indicates that when indeed non-perturbative
> > effects are taken into account, _most_ of the moduli do get stabilized.
>
> What is the KKLT paper, and how do most of the moduli get stabilized?
It's
Kachru & Kallosh & Linde & Trivedi:
de Sitter vacua in string theory
http://www.arxiv.org/abs/hep-th/0301240
which started most of the landscape discussion, as far as I am aware. For
a nice summary of some of the effects discussed in there see J. Distler's
"Digging up the landscape"
http://golem.ph.utexas.edu/~distler/blog/archives/000359.html
and
"The discretium"
http://golem.ph.utexas.edu/~distler/blog/archives/000348.html.
Also see the sci.physics.strings archive for the thread
"Conceptual question"
where Shamit Kachru himself, together with J. Polchinski and W. Lerche, L.
Motl and A. Rajaraman discuss this issue.
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Urs Schreiber <Urs.Schreiber@uni-essen.de> wrote in message news:<Pine.LNX.4.31.0405261029590.20392-100000@kaluza.harvard.edu>...\n> Yes, after posting that message I had this idea, too, that the autor is\n> probably thinking of the fact that the _Hamiltomnian constraint_ vanishes.\n> That\'s why he says "at least classically", being aware of the well\n> understood case of 1+1 dimensions where the Hamiltonian constraint (L0 +\n> \\bar L_0) is "0" only up a quantum shift.\n>\n> But if that\'s what the author is thinking of in that paragraph it really\n> makes me feel uneasy, because, as you indicated\n>\n> 1) the fact that the Hamiltonian constraint vanishes says little about the\n> energy content of the universe (much like (L_0-1)|psi>=0 alone tells me\n> nothing about the mass of a string state psi)\n>\n> 2) the statement does not have anything to do with the figure that\n> accompanies it and the conclusions drawn from it (please anyone correct\n> me if I am wrong about this!)\n>\n> > (matter) energy-momentum tensor, which is exactly the\n> > "non-vanishing energy content" you are talking about. It is the\n> > Hamiltonian, though, which is the relevant quantity for\n> > thermodynamical considerations.\n>\n> Yes, that\'s what I would think. And this Hamiltonian does not vanish.\n\nI tend to disagree with you. The only properly defined Hamiltonian\nhere is the Hamiltonian constraint (since we are in bounded space)\nand it _does_ vanish. I.e., instead of the usual Gibbs ensemble\nexp(-beta H) we get just the identity density matrix. Now, since\nentropy is monotonously decreasing with the cosmological constant\n(see equation 2.7 on page 7; note R is monotonously decreasing\nwith the cosmological constant) fluctuations from the metastable\nvacuum at phi_0 (see figure 1) will indeed be suppressed by pure\nentropy considerations.\n\n> It\'s\n>\n> Kachru & Kallosh & Linde & Trivedi:\n> de Sitter vacua in string theory\n> hep-th/0301240\n>\n> which started most of the landscape discussion, as far as I am aware. For\n> a nice summary of some of the effects discussed in there see J. Distler\'s\n>\n> "Digging up the landscape"\n> http://golem.ph.utexas.edu/~distler/blog/archives/000359.html\n>\n> and\n>\n> "The discretium"\n> http://golem.ph.utexas.edu/~distler/blog/archives/000348.html.\n>\n> Also see the sci.physics.strings archive for the thread\n>\n> "Conceptual question"\n>\n> where Shamit Kachru himself, together with J. Polchinski and W. Lerche, L.\n> Motl and A. Rajaraman discuss this issue.\n\nThx!\n\nBest regards,\nSquark.\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Urs Schreiber <Urs.Schreiber@uni-essen.de> wrote in message news:<Pine.LNX.4.31.0405261029590.20392-100000@kaluza.harvard.edu>...
> Yes, after posting that message I had this idea, too, that the autor is
> probably thinking of the fact that the _Hamiltomnian constraint_ vanishes.
> That's why he says "at least classically", being aware of the well
> understood case of 1+1 dimensions where the Hamiltonian constraint (L0 +
> \bar L_0) is "" only up a quantum shift.
>
> But if that's what the author is thinking of in that paragraph it really
> makes me feel uneasy, because, as you indicated
>
> 1) the fact that the Hamiltonian constraint vanishes says little about the
> energy content of the universe (much like (L_0-1)|\psi>=0 alone tells me
> nothing about the mass of a string state \psi)
>
> 2) the statement does not have anything to do with the figure that
> accompanies it and the conclusions drawn from it (please anyone correct
> me if I am wrong about this!)
>
> > (matter) energy-momentum tensor, which is exactly the
> > "non-vanishing energy content" you are talking about. It is the
> > Hamiltonian, though, which is the relevant quantity for
> > thermodynamical considerations.
>
> Yes, that's what I would think. And this Hamiltonian does not vanish.
I tend to disagree with you. The only properly defined Hamiltonian
here is the Hamiltonian constraint (since we are in bounded space)
and it _does_ vanish. I.e., instead of the usual Gibbs ensemble
\exp(-\beta H) we get just the identity density matrix. Now, since
entropy is monotonously decreasing with the cosmological constant
(see equation 2.7 on page 7; note R is monotonously decreasing
with the cosmological constant) fluctuations from the metastable
vacuum at \phi_0 (see figure 1) will indeed be suppressed by pure
entropy considerations.
> It's
>
> Kachru & Kallosh & Linde & Trivedi:
> de Sitter vacua in string theory
> http://www.arxiv.org/abs/hep-th/0301240
>
> which started most of the landscape discussion, as far as I am aware. For
> a nice summary of some of the effects discussed in there see J. Distler's
>
> "Digging up the landscape"
> http://golem.ph.utexas.edu/~distler/blog/archives/000359.html
>
> and
>
> "The discretium"
> http://golem.ph.utexas.edu/~distler/blog/archives/000348.html.
>
> Also see the sci.physics.strings archive for the thread
>
> "Conceptual question"
>
> where Shamit Kachru himself, together with J. Polchinski and W. Lerche, L.
> Motl and A. Rajaraman discuss this issue.
Thx!
Best regards,
Squark.
Urs Schreiber
May30-04, 07:30 PM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>"Squark" <fiis5d@yahoo.com> schrieb im Newsbeitrag\nnews:939044f.0405301126.ce337e0-100000@posting.google.com...\n\n> I tend to disagree with you. The only properly defined Hamiltonian\n> here is the Hamiltonian constraint (since we are in bounded space)\n> and it _does_ vanish.\n\nThe Hamiltonian constraint is a "Hamiltonian" only in the sense of a formal\nanalogy: The "evolution" it generates is reparameterization, something\ncompletely unphysical. Of course you may think of a canonical ensemble with\nthe weight exp(- beta times Hamiltonian constraint), but that\'s just as\nmeaningful as considering the weight exp(- beta 12), it\'s just a constant\nwhich can be reabsorbed.\n\nBut there _is_ a properly defined canonical ensemble for the true time\nevolution of a gravitational system, and it is that of relativistic\nthermodynamics of the relativistic dynamics in _configuration space_ (which\nis nothing but moduli space is the generalized sense used by Susskind).\n\nIt is crucial to note that when gravity is rewritten in Hamiltonian form it\ndescribes the evolution of the configuration point in configurations space,\nand that in particular it induces a pseudo-Riemannian metric of signature\n(-,+,+,+,+,...) on this configuration space with the scale factor of the\nuniverse associated with the direction of negative signature. The\nHamiltonian constraint Ham is a generalized Laplace operator (when\nquantized) on this pseudo-Riemannian manifold and the equation\n\nHam = 0\n\nis nothing but the (generalized) Klein-Gordon-like wave equation on config\nspace.\n\nThis evolution in general preserves certain quantities. For instance if\nthere is no explicit "potential" then every Killing vector (on configuration\nspace!) implies a conserved quantity and can be written into the exponent of\nthe canonical ensemble.\n\nIf you take the free Klein-Gordon particle on flat spacetime as a simple\nexample of a relativistic system of this form it would have a coninical\nensemble ~ exp(- \\beta^\\mu p_\\mu), for instance, where p_\\mu are the momenta\nassociated to to the translational Killing vectors of flat space. p_0 of\ncourse is the guy measuring the energy, which takes the place of H for\nnon-relativistic systems in the canonical ensemble.\n\nSo what one would really need to do in order to make the statistical\nconcepts used in the landscape discussion moderately precise is to consider\nsome quasi-accurate total Lagrangian of the systems that one wants to\nstatistic with, e.g. that of supergravity plus maybe that of some further\ndegees of freedom like branes, etc., compute the metric on configuration\nspace and the potentials on coinfiguration space implied by this Lagrangian,\nfigure out the Killing vectors in config space which respect the potentials,\nand then construct the canonical ensemble with respect to these conserved\nquantities, as described above for the analogous toy example of the KG\nparticle.\n\nIn cosmologies that are studied ordinarily most config space potentials\nactually depend on the scale factor of the universe and are hence\n"configuration-time"-dependent. In these cases there would indeed be no\nconserved "energy" in config space, and hence the canonical ensemble might\nhave no suppression factor at all, the way that Susskind imagines it to be.\n\nBut experience shows that in unified theories things that look like\nconfig-space-potentials in ordinary cosmology tend to become effective\npotential, which are really kinetic terms for further degrees of freedom.\nThis suggests that one should in general expect more conserved config space\nquantities.\n\nFor instance if the conjecture is correct, that M-theory is fully described\nby the sigma model on exp(E10), then the above mentioned configuration space\nis nothing but this exp(E10) and everything that might appear as a potential\nis just the kinetic term of one of the many degrees of freedom. In this case\nthere are in fact infinitely many Killing vectors/conserved quantities for\nthe evolution of the universe, which should all enter into the exponent of\nthe canonical ensemble. In particular one of the conserved quantities\nmeasures the momentum along the minus-signature direction on exp(E10), and\nhence the energy.\n\nFor these reasons I would really expect an energy suppression factor for the\nlandscape statistics.\n\n\n\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>"Squark" <fiis5d@yahoo.com> schrieb im Newsbeitrag
news:939044f.0405301126.ce337e0-100000@posting.google.com...
> I tend to disagree with you. The only properly defined Hamiltonian
> here is the Hamiltonian constraint (since we are in bounded space)
> and it _does_ vanish.
The Hamiltonian constraint is a "Hamiltonian" only in the sense of a formal
analogy: The "evolution" it generates is reparameterization, something
completely unphysical. Of course you may think of a canonical ensemble with
the weight \exp(- \beta times Hamiltonian constraint), but that's just as
meaningful as considering the weight \exp(- \beta 12), it's just a constant
which can be reabsorbed.
But there _is_ a properly defined canonical ensemble for the true time
evolution of a gravitational system, and it is that of relativistic
thermodynamics of the relativistic dynamics in _configuration space_ (which
is nothing but moduli space is the generalized sense used by Susskind).
It is crucial to note that when gravity is rewritten in Hamiltonian form it
describes the evolution of the configuration point in configurations space,
and that in particular it induces a pseudo-Riemannian metric of signature
(-,+,+,+,+,...) on this configuration space with the scale factor of the
universe associated with the direction of negative signature. The
Hamiltonian constraint Ham is a generalized Laplace operator (when
quantized) on this pseudo-Riemannian manifold and the equation
Ham =
is nothing but the (generalized) Klein-Gordon-like wave equation on config
space.
This evolution in general preserves certain quantities. For instance if
there is no explicit "potential" then every Killing vector (on configuration
space!) implies a conserved quantity and can be written into the exponent of
the canonical ensemble.
If you take the free Klein-Gordon particle on flat spacetime as a simple
example of a relativistic system of this form it would have a coninical
ensemble ~ \exp(- \beta^\mu p_\mu), for instance, where p_\mu are the momenta
associated to to the translational Killing vectors of flat space. p_0 of
course is the guy measuring the energy, which takes the place of H for
non-relativistic systems in the canonical ensemble.
So what one would really need to do in order to make the statistical
concepts used in the landscape discussion moderately precise is to consider
some quasi-accurate total Lagrangian of the systems that one wants to
statistic with, e.g. that of supergravity plus maybe that of some further
degees of freedom like branes, etc., compute the metric on configuration
space and the potentials on coinfiguration space implied by this Lagrangian,
figure out the Killing vectors in config space which respect the potentials,
and then construct the canonical ensemble with respect to these conserved
quantities, as described above for the analogous toy example of the KG
particle.
In cosmologies that are studied ordinarily most config space potentials
actually depend on the scale factor of the universe and are hence
"configuration-time"-dependent. In these cases there would indeed be no
conserved "energy" in config space, and hence the canonical ensemble might
have no suppression factor at all, the way that Susskind imagines it to be.
But experience shows that in unified theories things that look like
config-space-potentials in ordinary cosmology tend to become effective
potential, which are really kinetic terms for further degrees of freedom.
This suggests that one should in general expect more conserved config space
quantities.
For instance if the conjecture is correct, that M-theory is fully described
by the \sigma model on \exp(E10), then the above mentioned configuration space
is nothing but this \exp(E10) and everything that might appear as a potential
is just the kinetic term of one of the many degrees of freedom. In this case
there are in fact infinitely many Killing vectors/conserved quantities for
the evolution of the universe, which should all enter into the exponent of
the canonical ensemble. In particular one of the conserved quantities
measures the momentum along the minus-signature direction on \exp(E10), and
hence the energy.
For these reasons I would really expect an energy suppression factor for the
landscape statistics.
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Urs Schreiber <Urs.Schreiber@uni-essen.de> wrote in message news:<2hv93tFhmhjuU1-100000@uni-berlin.de>...\n\n> But there _is_ a properly defined canonical ensemble for the true time\n> evolution of a gravitational system, and it is that of relativistic\n> thermodynamics of the relativistic dynamics in _configuration space_ (which\n> is nothing but moduli space is the generalized sense used by Susskind).\n\nWhat precisely is the configuration space you are talking about? You\nrelate it to the moduli space, so I suppose you\'re mainly talking about\nthe geometry of the compactified dimensions here? This is not a\nmeaningful observable when you\'re talking about compact space. In the\nasymptotically flat case you could consider the asymptotic form of the\ncompactified dimensions geometry and define its dynamics. Then you in\nfact use the Hamiltonian associated with time translations w.r.t. the\ntime of the observer at infinity. Nothing like this makes sense for\ncompact space.\n\nNote that Susskind is of course not assuming space per se is compact\nbut he\'s considering a single casual (horizon-bounded) patch in a\nuniverse expanding with acceleration (like hours).\n\n> For instance if the conjecture is correct, that M-theory is fully described\n> by the sigma model on exp(E10), then the above mentioned configuration space\n> is nothing but this exp(E10) and everything that might appear as a potential\n> is just the kinetic term of one of the many degrees of freedom.\n\nWhat\'s exp(E10) and whence this conjecture?\n\nBest regards,\nSquark\n\n[This posting was re-posted again after the Harvard FAS newsserver\nproblems on June 2nd. LM]\n\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Urs Schreiber <Urs.Schreiber@uni-essen.de> wrote in message news:<2hv93tFhmhjuU1-100000@uni-berlin.de>...
> But there _is_ a properly defined canonical ensemble for the true time
> evolution of a gravitational system, and it is that of relativistic
> thermodynamics of the relativistic dynamics in _configuration space_ (which
> is nothing but moduli space is the generalized sense used by Susskind).
What precisely is the configuration space you are talking about? You
relate it to the moduli space, so I suppose you're mainly talking about
the geometry of the compactified dimensions here? This is not a
meaningful observable when you're talking about compact space. In the
asymptotically flat case you could consider the asymptotic form of the
compactified dimensions geometry and define its dynamics. Then you in
fact use the Hamiltonian associated with time translations w.r.t. the
time of the observer at infinity. Nothing like this makes sense for
compact space.
Note that Susskind is of course not assuming space per se is compact
but he's considering a single casual (horizon-bounded) patch in a
universe expanding with acceleration (like hours).
> For instance if the conjecture is correct, that M-theory is fully described
> by the \sigma model on \exp(E10), then the above mentioned configuration space
> is nothing but this \exp(E10) and everything that might appear as a potential
> is just the kinetic term of one of the many degrees of freedom.
What's \exp(E10) and whence this conjecture?
Best regards,
Squark
[This posting was re-posted again after the Harvard FAS newsserver
problems on June 2nd. LM]
Urs Schreiber
Jun3-04, 12:14 PM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>NNTP-Posting-Host: feynman.harvard.edu\nMime-Version: 1.0\nContent-Type: TEXT/PLAIN; charset=US-ASCII\nX-Trace: us23.unix.fas.harvard.edu 1086279304 4132 140.247.123.226 (3 Jun 2004 16:15:04 GMT)\nX-Complaints-To: usenet@news.fas.harvard.edu\nNNTP-Posting-Date: Thu, 3 Jun 2004 16:15:04 +0000 (UTC)\nX-X-Sender: <sps@feynman.harvard.edu>\nIn-Reply-To: <939044f.0406020851.6f32be4f-100000@posting.google.com>\nXref: solaris.cc.vt.edu sci.physics.strings:323\n\nOn Wed, 2 Jun 2004, Squark wrote:\n\n> What precisely is the configuration space that you are talking about?\n\nBy the ADM method config space is the space of field configurations on\nspatial hyperslices - Wheeler\'s "superspace" (not that of supersymmetry) or\nsome min- or midi- superspace approximation thereof, retaining only a finite\nnumber of degrees of freedom\n\nUsing the ADM procedure you rewrite the action in terms of purely\ntime-dependent mode amplitudes. The space in which these mode amplitudes\ntake their values is configuration space. (This is just the usual procedure\nthat you can find described in any text on (quantum) cosmology).\n\nOn pp. 268 of http://www-stud.uni-essen.de/~sb0264/sqm.pdf I had worked out\nhow this works for a very simple (very naive, actually) reduced form of the\nbosonic sector of 11d SUGRA compactified on T^7 with homogeneous fluxes\nturned on.\n\n(I have assumed all of space to be compact, for simplicity. As you point\nout, if we have some flat asymptotics we can define a time translation with\nrespect to the asymptotic time parameter. But in this case, too, the\nBoltzmann wheight would not be unity identically.)\n\n\n> What\'s exp(E10) and whence this conjecture?\n\n\nexp(E10) is shorthand for the "group" associated with the hyperbolic\nKac-Moody algabra E10.\n\nOne reason to conjecture that this humongous group is the full configuration\nspace of M-theory is that apparently the full dynamics of 11D sugra is\nobtained by geodesic motion in a (small) subsector of this group. J. Brown\net al have some tantalizing arguments that the remaining degees of freedom\nencoded in exp(E10) do indeed describe the brane DOFs of full M-theory.\n\nFor a basic introduction of some of the ideas that motivate this see the\nentry\n\nhttp://golem.ph.utexas.edu/string/archives/000353.html\n\nand the literature given here:\n\nhttp://golem.ph.utexas.edu/string/archives/000327.html#c000953 .\n\n\nSee also our discussion of this topic at sci.physics.strings:\n\nhttp://physicsforums.com/showthread.php?t=20864\n\n[This posting was re-posted again after the Harvard FAS newsserver\nproblems on June 2nd. LM]\n\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>NNTP-Posting-Host: feynman.harvard.edu
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Xref: solaris.cc.vt.edu sci.physics.strings:323
On Wed, 2 Jun 2004, Squark wrote:
> What precisely is the configuration space that you are talking about?
By the ADM method config space is the space of field configurations on
spatial hyperslices - Wheeler's "superspace" (not that of supersymmetry) or
some min- or midi- superspace approximation thereof, retaining only a finite
number of degrees of freedom
Using the ADM procedure you rewrite the action in terms of purely
time-dependent mode amplitudes. The space in which these mode amplitudes
take their values is configuration space. (This is just the usual procedure
that you can find described in any text on (quantum) cosmology).
On pp. 268 of http://www-stud.uni-essen.de/~sb0264/sqm.pdf I had worked out
how this works for a very simple (very naive, actually) reduced form of the
bosonic sector of 11d SUGRA compactified on T^7 with homogeneous fluxes
turned on.
(I have assumed all of space to be compact, for simplicity. As you point
out, if we have some flat asymptotics we can define a time translation with
respect to the asymptotic time parameter. But in this case, too, the
Boltzmann wheight would not be unity identically.)
> What's \exp(E10) and whence this conjecture?
\exp(E10) is shorthand for the "group" associated with the hyperbolic
Kac-Moody algabra E10.
One reason to conjecture that this humongous group is the full configuration
space of M-theory is that apparently the full dynamics of 11D sugra is
obtained by geodesic motion in a (small) subsector of this group. J. Brown
et al have some tantalizing arguments that the remaining degees of freedom
encoded in \exp(E10) do indeed describe the brane DOFs of full M-theory.
For a basic introduction of some of the ideas that motivate this see the
entry
http://golem.ph.utexas.edu/string/archives/000353.html
and the literature given here:
http://golem.ph.utexas.edu/string/archives/000327.html#c000953 .
See also our discussion of this topic at sci.physics.strings:
http://physicsforums.com/showthread.php?t=20864
[This posting was re-posted again after the Harvard FAS newsserver
problems on June 2nd. LM]
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Urs Schreiber wrote in message news:<Pine.LNX.4.31.0406031214100.16355-100000@feynman.harvard.edu>...\n\n> On Wed, 2 Jun 2004, Squark wrote:\n>\n> > What precisely is the configuration space that you are talking about?\n>\n> By the ADM method config space is the space of field configurations on\n> spatial hyperslices - Wheeler\'s "superspace" (not that of supersymmetry) or\n> some min- or midi- superspace approximation thereof, retaining only a finite\n> number of degrees of freedom\n\nNow I see what you\'re talking about. Well, a Killing vector\nin this configuration space is essentially a continous global\nsymmetry of the theory. However, Michael Douglas writes in\n"The statistics of M-theory vacua" (hep-th/0303194), page 12,\nthat probably no such continous global symmetry exists. The\narticle he is referring to (T.Banks and L.J.Dixon, Nuclear\nPhysics, B307, 93) dates back to 1988 and is not avaible on\nthe net, as far as I know, so unfortunatelly I have no access\nto it currently. I certainly know about no such symmetry. The\none argument I can think about against it is that it would be\nassociated with a conserved charged whose existence in a\ngravitational theory conflicts the no-hair theorem.\n\n> exp(E10) is shorthand for the "group" associated with the hyperbolic\n> Kac-Moody algabra E10.\n>\n> One reason to conjecture that this humongous group is the full configuration\n> space of M-theory is that apparently the full dynamics of 11D sugra is\n> obtained by geodesic motion in a (small) subsector of this group.\n\nI haven\'t peeked at the references you supplied yet, but it\nis far from obvious what would be meant by "the full\nconfiguration space pf M-theory". According to the\ndefinition you gave earlier, (classical) gravitational\ndynamics would not generate trajectories in this\nconfiguration space but rather subspaces of\ninfinite dimension (and codimension), each such subspace\ncorresponding to all of the spacelike slices of a given\nsolution. I\'d say the system is not described by a particle\nin configuration space but rather by and infinity-brane!\n\nBest regards,\nSquark.\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Urs Schreiber wrote in message news:<Pine.LNX.4.31.0406031214100.16355-100000@feynman.harvard.edu>...
> On Wed, 2 Jun 2004, Squark wrote:
>
> > What precisely is the configuration space that you are talking about?
>
> By the ADM method config space is the space of field configurations on
> spatial hyperslices - Wheeler's "superspace" (not that of supersymmetry) or
> some min- or midi- superspace approximation thereof, retaining only a finite
> number of degrees of freedom
Now I see what you're talking about. Well, a Killing vector
in this configuration space is essentially a continous global
symmetry of the theory. However, Michael Douglas writes in
"The statistics of M-theory vacua" (http://www.arxiv.org/abs/hep-th/0303194), page 12,
that probably no such continous global symmetry exists. The
article he is referring to (T.Banks and L.J.Dixon, Nuclear
Physics, B307, 93) dates back to 1988 and is not avaible on
the net, as far as I know, so unfortunatelly I have no access
to it currently. I certainly know about no such symmetry. The
one argument I can think about against it is that it would be
associated with a conserved charged whose existence in a
gravitational theory conflicts the no-hair theorem.
> \exp(E10) is shorthand for the "group" associated with the hyperbolic
> Kac-Moody algabra E10.
>
> One reason to conjecture that this humongous group is the full configuration
> space of M-theory is that apparently the full dynamics of 11D sugra is
> obtained by geodesic motion in a (small) subsector of this group.
I haven't peeked at the references you supplied yet, but it
is far from obvious what would be meant by "the full
configuration space pf M-theory". According to the
definition you gave earlier, (classical) gravitational
dynamics would not generate trajectories in this
configuration space but rather subspaces of
infinite dimension (and codimension), each such subspace
corresponding to all of the spacelike slices of a given
solution. I'd say the system is not described by a particle
in configuration space but rather by and infinity-brane!
Best regards,
Squark.
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