View Full Version : [SOLVED] Tachyons can change topology
Lubos Motl
Feb2-05, 09:03 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>http://motls.blogspot.com/2005/02/tachyons-can-change-topology.html\n=================================== ================================\n\nIn the last 2 hours, Allan Adams just told us about his supernew paper\n\n* Adams, Liu, McGreevy, Saltman, Silverstein\n\nand because I think that it is definitely an interesting paper, let me say\na couple of words.\n\nImagine that you take a type II string theory and compactify it down to 8\ndimensions, on a two-dimensional genus "g" Riemann surface.\n\nWell, unless "g=1", it is a non-conformal theory, so you will have to deal\nwith a time-dependent background. Let\'s not worry. Let\'s assume the string\ncoupling to be weak throughout the story.\n\nImagine that you start with a genus 2 Riemann surface. It can degenerate\ninto two genus 1 Riemann surfaces connected by a thin tube. The circle\nwrapped around this tube is homologically trivial, and you can show that\nthe fermions will be antiperiodic around it: it will be a\nScherk-Schwarz/Rohm compactification on a thermal circle. The reason for\nthe antiperiodicity is the same like the reason that the closed strings in\nthe NS-NS sector must have antiperiodic boundary conditions for the\nfermions assuming that the corresponding operators in the "z" plane don\'t\nintroduce any branch cuts.\n\nOK, imagine that the tube is very long. Because of the antiperiodic\nboundary conditions, the sign of the GSO condition in the sectors with odd\nwindings is reverted, and one can find some tachyons there assuming that\nthe radius is small enough so that the winding is not enough to make the\nsquared mass positive. Equivalently, one can T-dualize along the\ncircumference of the tube to obtain some sort of type 0 theory which has a\nbulk tachyon if the radius in the type 0 picture is large enough. Go\nexactly near the point where the first tachyon in the "w=1" sector starts\nto evolve. It\'s the first perturbative instability you encounter.\n\nThese guys then argue that the most obvious time evolution will take\nplace. The tachyons start to get condensed, and the handle will pinch off.\nIt can be seen as a perturbative instability although it is probably\ncontinuously connected to the non-perturbative stability called the Witten\nbubble, and they use various CFT techniques, Ricci flows, RG flows, N=1\nand N=2 worldsheet supersymmetry to study the process quantitatively. They\nargue that the two ends of the tube don\'t talk to each other - the strings\ncan\'t propagate through the critical region where the topology change\ntakes place. I am not gonna write the math here because you can open the\npaper.\n\nSuch a process can reduce the genus of a Riemann surface. Recall the\npicture with Brian Greene\'s breakfast on PBS/NOVA: the topology of the\ncoffee cup and the doughnut are identical, but once Brian bites doughnut,\nit is going to become a sphere. In this case, the TV program is exact, not\njust a lower-dimensional analogy of the conifold transition. ;-)\n\nThe same process, however, can divide a higher genus Riemann surface into\npieces that don\'t interact at all. The world decays into pieces - baby\nuniverses and similar stuff. A lot of interesting stuff happens from the\nlow-energy effective theory viewpoint - doubling of gravity, decoupling of\nvarious modes, gaps emerging and disappearing, and many other things. Note\nthat spacetime supersymmetry is broken, but one can arrange the parameters\nof the geometry in such a way that the evolution is more or less\ncontrollable.\n\nI still believe that similar kinds of topology changing transitions may\neventually destabilize or eliminate most of the "landscape". If you start\nwith a too convoluted Calabi-Yau space with fluxes, there will be many\nmodes how it can decay - it is potentially able to split into two (or\nmore) Calabi-Yau pieces. Instead of the 2-dimensional handles of the\ncylindrical type, there may be many higher-dimensional analogues of the\ncylinder although most of us so far seem to have trouble to find working\nhigher-dimensional examples. Such processes do not have to be too likely,\nbut there are just many channels in which such a complicated Calabi-Yau\nspace can decay - the number of channels is large because the number of\n"simpler" minima in the landscape is claimed to be large as well. This\nlargeness is, I believe, self-destructive for the landscape.\n\nMy intuition is that such a decay tends to simplify the homology of both\nfinal products - i.e. reduce their Hodge numbers. This is a reason to\nbelieve that the Calabi-Yaus with very small Hodge numbers will be\npreferred. Braun, He, Ovrut, Pantev have found a quasi-unique heterotic\nstandard model based on a Calabi-Yau with h^{1,1}=h^{2,1}=3. Three is the\nsmallest positive integer after one and two - a pretty good choice.\nAssuming that there is something right about this and previous paragraph,\nBraun et al. have a pretty good chance that they have found the theory of\neverything. ;-)\n\nMeanwhile, Adams et al. have made useful steps to understand tachyons in\nstring theory. Note that these new understood tachyons start to look like\nbulk tachyons. The first understood tachyons were open tachyons (Sen and\nothers); then people (APS; but also Headrick) continued with the closed\nstring twisted tachyons; now they\'re getting into the bulk.\n\nComments welcome.\n________________________________________ ______________________________________\nE-mail: lumo@matfyz.cz fax: +1-617/496-0110 Web: http://lumo.matfyz.cz/\neFax: +1-801/454-1858 work: +1-617/384-9488 home: +1-617/868-4487 (call)\nWebs: http://schwinger.harvard.edu/~motl/ http://motls.blogspot.com/\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>http://motls.blogspot.com/2005/02/tachyons-can-change-topology.html
================================================== =================
In the last 2 hours, Allan Adams just told us about his supernew paper
* Adams, Liu, McGreevy, Saltman, Silverstein
and because I think that it is definitely an interesting paper, let me say
a couple of words.
Imagine that you take a type II string theory and compactify it down to 8
dimensions, on a two-dimensional genus "g" Riemann surface.
Well, unless "g=1", it is a non-conformal theory, so you will have to deal
with a time-dependent background. Let's not worry. Let's assume the string
coupling to be weak throughout the story.
Imagine that you start with a genus 2 Riemann surface. It can degenerate
into two genus 1 Riemann surfaces connected by a thin tube. The circle
wrapped around this tube is homologically trivial, and you can show that
the fermions will be antiperiodic around it: it will be a
Scherk-Schwarz/Rohm compactification on a thermal circle. The reason for
the antiperiodicity is the same like the reason that the closed strings in
the NS-NS sector must have antiperiodic boundary conditions for the
fermions assuming that the corresponding operators in the "z" plane don't
introduce any branch cuts.
OK, imagine that the tube is very long. Because of the antiperiodic
boundary conditions, the sign of the GSO condition in the sectors with odd
windings is reverted, and one can find some tachyons there assuming that
the radius is small enough so that the winding is not enough to make the
squared mass positive. Equivalently, one can T-dualize along the
circumference of the tube to obtain some sort of type theory which has a
bulk tachyon if the radius in the type picture is large enough. Go
exactly near the point where the first tachyon in the "w=1" sector starts
to evolve. It's the first perturbative instability you encounter.
These guys then argue that the most obvious time evolution will take
place. The tachyons start to get condensed, and the handle will pinch off.
It can be seen as a perturbative instability although it is probably
continuously connected to the non-perturbative stability called the Witten
bubble, and they use various CFT techniques, Ricci flows, RG flows, N=1
and N=2 worldsheet supersymmetry to study the process quantitatively. They
argue that the two ends of the tube don't talk to each other - the strings
can't propagate through the critical region where the topology change
takes place. I am not gonna write the math here because you can open the
paper.
Such a process can reduce the genus of a Riemann surface. Recall the
picture with Brian Greene's breakfast on PBS/NOVA: the topology of the
coffee cup and the doughnut are identical, but once Brian bites doughnut,
it is going to become a sphere. In this case, the TV program is exact, not
just a lower-dimensional analogy of the conifold transition. ;-)
The same process, however, can divide a higher genus Riemann surface into
pieces that don't interact at all. The world decays into pieces - baby
universes and similar stuff. A lot of interesting stuff happens from the
low-energy effective theory viewpoint - doubling of gravity, decoupling of
various modes, gaps emerging and disappearing, and many other things. Note
that spacetime supersymmetry is broken, but one can arrange the parameters
of the geometry in such a way that the evolution is more or less
controllable.
I still believe that similar kinds of topology changing transitions may
eventually destabilize or eliminate most of the "landscape". If you start
with a too convoluted Calabi-Yau space with fluxes, there will be many
modes how it can decay - it is potentially able to split into two (or
more) Calabi-Yau pieces. Instead of the 2-dimensional handles of the
cylindrical type, there may be many higher-dimensional analogues of the
cylinder although most of us so far seem to have trouble to find working
higher-dimensional examples. Such processes do not have to be too likely,
but there are just many channels in which such a complicated Calabi-Yau
space can decay - the number of channels is large because the number of
"simpler" minima in the landscape is claimed to be large as well. This
largeness is, I believe, self-destructive for the landscape.
My intuition is that such a decay tends to simplify the homology of both
final products - i.e. reduce their Hodge numbers. This is a reason to
believe that the Calabi-Yaus with very small Hodge numbers will be
preferred. Braun, He, Ovrut, Pantev have found a quasi-unique heterotic
standard model based on a Calabi-Yau with h^{1,1}=h^{2,1}=3. Three is the
smallest positive integer after one and two - a pretty good choice.
Assuming that there is something right about this and previous paragraph,
Braun et al. have a pretty good chance that they have found the theory of
everything. ;-)
Meanwhile, Adams et al. have made useful steps to understand tachyons in
string theory. Note that these new understood tachyons start to look like
bulk tachyons. The first understood tachyons were open tachyons (Sen and
others); then people (APS; but also Headrick) continued with the closed
string twisted tachyons; now they're getting into the bulk.
Comments welcome.
__{_______________________________________________ _____________________________}
E-mail: lumo@matfyz.cz fax: +1-617/496-0110 Web: http://lumo.matfyz.cz/
eFax: +1-801/454-1858 work: +1-617/384-9488 home: +1-617/868-4487 (call)
Webs: http://schwinger.harvard.edu/~motl/ http://motls.blogspot.com/
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Urs Schreiber
Feb3-05, 03:15 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>On Wed, 2 Feb 2005, Lubos Motl wrote:\n\n\n> I still believe that similar kinds of topology changing transitions may\n> eventually destabilize or eliminate most of the "landscape". If you start\n> with a too convoluted Calabi-Yau space with fluxes, there will be many\n> modes how it can decay - it is potentially able to split into two (or\n> more) Calabi-Yau pieces.\n\n\nThat sounds interesting. Is this just a guess or are there specific\nindications that the work that you summarized should generalize this way?\n\n\n> My intuition is that such a decay tends to simplify the homology of both\n> final products - i.e. reduce their Hodge numbers. This is a reason to\n> believe that the Calabi-Yaus with very small Hodge numbers will be\n> preferred. Braun, He, Ovrut, Pantev have found a quasi-unique heterotic\n> standard model based on a Calabi-Yau with h^{1,1}=h^{2,1}=3. Three is the\n> smallest positive integer after one and two - a pretty good choice.\n> Assuming that there is something right about this and previous paragraph,\n> Braun et al. have a pretty good chance that they have found the theory of\n> everything. ;-)\n\n\nThis was discussed already in another thread, but there I forgot to ask:\n\nIn which sense is the model "quasi-unique"? (I haven\'t even looked at the\npaper yet.) I guess there are some natural assumptions A,B,C,... which\nare satisfied only by that particular CY? What are these assumptions?\n\n\n> Meanwhile, Adams et al. have made useful steps to understand tachyons in\n> string theory. Note that these new understood tachyons start to look like\n> bulk tachyons. The first understood tachyons were open tachyons (Sen and\n> others); then people (APS; but also Headrick) continued with the closed\n> string twisted tachyons; now they\'re getting into the bulk.\n\n\nIs this about closed bosonic string tachyons?\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, 2 Feb 2005, Lubos Motl wrote:
> I still believe that similar kinds of topology changing transitions may
> eventually destabilize or eliminate most of the "landscape". If you start
> with a too convoluted Calabi-Yau space with fluxes, there will be many
> modes how it can decay - it is potentially able to split into two (or
> more) Calabi-Yau pieces.
That sounds interesting. Is this just a guess or are there specific
indications that the work that you summarized should generalize this way?
> My intuition is that such a decay tends to simplify the homology of both
> final products - i.e. reduce their Hodge numbers. This is a reason to
> believe that the Calabi-Yaus with very small Hodge numbers will be
> preferred. Braun, He, Ovrut, Pantev have found a quasi-unique heterotic
> standard model based on a Calabi-Yau with h^{1,1}=h^{2,1}=3. Three is the
> smallest positive integer after one and two - a pretty good choice.
> Assuming that there is something right about this and previous paragraph,
> Braun et al. have a pretty good chance that they have found the theory of
> everything. ;-)
This was discussed already in another thread, but there I forgot to ask:
In which sense is the model "quasi-unique"? (I haven't even looked at the
paper yet.) I guess there are some natural assumptions A,B,C,... which
are satisfied only by that particular CY? What are these assumptions?
> Meanwhile, Adams et al. have made useful steps to understand tachyons in
> string theory. Note that these new understood tachyons start to look like
> bulk tachyons. The first understood tachyons were open tachyons (Sen and
> others); then people (APS; but also Headrick) continued with the closed
> string twisted tachyons; now they're getting into the bulk.
Is this about closed bosonic string tachyons?
<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>Lubos wrote:\n\n"I still believe that similar kinds of topology changing transitions\nmay eventually destabilize or eliminate most of the "landscape".\nIf you start with a too convoluted Calabi-Yau space with fluxes,\nthere will be many modes how it can decay - it is potentially able\nto split into two (or more) Calabi-Yau pieces. Instead of the\n2-dimensional handles of the cylindrical type, there may be many\nhigher-dimensional analogues of the cylinder although most of us\nso far seem to have trouble to find working higher-dimensional\nexamples. Such processes do not have to be too likely, but there\nare just many channels in which such a complicated Calabi-Yau space\ncan decay - the number of channels is large because the number of\n"simpler" minima in the landscape is claimed to be large as well.\nThis largeness is, I believe, self-destructive for the landscape.\n"\n\nI wouldn\'t see why such a decay would be energetically possible -\nwhere are the tachyons in CY compactifications ? Ordinary CY\ncompactifications tend to have supersymmetric vacuum states with\nenergy zero, so why should anything decay ? And BTW, it is known\nthat all CY\'s are connected by extremal transitions and so are\n(non-perturbatively) continuously connected - no need to talk about\ntachyons here.\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>Lubos wrote:
"I still believe that similar kinds of topology changing transitions
may eventually destabilize or eliminate most of the "landscape".
If you start with a too convoluted Calabi-Yau space with fluxes,
there will be many modes how it can decay - it is potentially able
to split into two (or more) Calabi-Yau pieces. Instead of the
2-dimensional handles of the cylindrical type, there may be many
higher-dimensional analogues of the cylinder although most of us
so far seem to have trouble to find working higher-dimensional
examples. Such processes do not have to be too likely, but there
are just many channels in which such a complicated Calabi-Yau space
can decay - the number of channels is large because the number of
"simpler" minima in the landscape is claimed to be large as well.
This largeness is, I believe, self-destructive for the landscape.
"
I wouldn't see why such a decay would be energetically possible -
where are the tachyons in CY compactifications ? Ordinary CY
compactifications tend to have supersymmetric vacuum states with
energy zero, so why should anything decay ? And BTW, it is known
that all CY's are connected by extremal transitions and so are
(non-perturbatively) continuously connected - no need to talk about
tachyons here.
Lubos Motl
Feb3-05, 11:07 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 Thu, 3 Feb 2005, Urs Schreiber wrote:\n\n> That sounds interesting. Is this just a guess or are there specific\n> indications that the work that you summarized should generalize this way?\n\nUnfortunately, it is my private comment and I have no particular geometric\n& quantitative models for the scenario at this moment. In fact, one can\nshow that various "easy to imagine" instabilities with respect to topology\nchange are certainly absent - for example, they are absent in the AdS SUSY\nvacua themselves, aren\'t they? There is nothing like the generalized\nantiperiodic boundary conditions of the fermions around a "tube".\n\nIs it excluded that the KKLT extra anti-D3-branes, for example, that turn\nAdS into dS, may lead to some mixed instantons that both change the\ntopology but also do something about the fluxes?\n\n> In which sense is the model "quasi-unique"? (I haven\'t even looked at the\n> paper yet.) I guess there are some natural assumptions A,B,C,... which\n> are satisfied only by that particular CY? What are these assumptions?\n\nIt is the only model within a big program of these authors that contains\nMSSM only at low energies, without new exotics (unobserved particles\ncharged under the Standard Model group, such as "leptoquarks"). You should\nread their paper(s).\n\n> Is this about closed bosonic string tachyons?\n\nWas my text so terribly incomprehensible, or did you reply without reading\neven my simplified abstract? It\'s type II string theory compactified on a\nRiemann surface down to 8 dimensions. At the long tubes, it is equivalent\nto type 0 theory by T-duality. It\'s still important that the tachyon\ncondensation only starts when the thickness of the tube decreases below a\ncritical value - there should not be any "truly" bulk tachyon (such as one\nin bosonic string theory), otherwise their new paper has nothing to say\nabout it.\n_____________________________________________ _________________________________\nE-mail: lumo@matfyz.cz fax: +1-617/496-0110 Web: http://lumo.matfyz.cz/\neFax: +1-801/454-1858 work: +1-617/384-9488 home: +1-617/868-4487 (call)\nWebs: http://schwinger.harvard.edu/~motl/ http://motls.blogspot.com/\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 Thu, 3 Feb 2005, Urs Schreiber wrote:
> That sounds interesting. Is this just a guess or are there specific
> indications that the work that you summarized should generalize this way?
Unfortunately, it is my private comment and I have no particular geometric
& quantitative models for the scenario at this moment. In fact, one can
show that various "easy to imagine" instabilities with respect to topology
change are certainly absent - for example, they are absent in the AdS SUSY
vacua themselves, aren't they? There is nothing like the generalized
antiperiodic boundary conditions of the fermions around a "tube".
Is it excluded that the KKLT extra anti-D3-branes, for example, that turn
AdS into dS, may lead to some mixed instantons that both change the
topology but also do something about the fluxes?
> In which sense is the model "quasi-unique"? (I haven't even looked at the
> paper yet.) I guess there are some natural assumptions A,B,C,... which
> are satisfied only by that particular CY? What are these assumptions?
It is the only model within a big program of these authors that contains
MSSM only at low energies, without new exotics (unobserved particles
charged under the Standard Model group, such as "leptoquarks"). You should
read their paper(s).
> Is this about closed bosonic string tachyons?
Was my text so terribly incomprehensible, or did you reply without reading
even my simplified abstract? It's type II string theory compactified on a
Riemann surface down to 8 dimensions. At the long tubes, it is equivalent
to type theory by T-duality. It's still important that the tachyon
condensation only starts when the thickness of the tube decreases below a
critical value - there should not be any "truly" bulk tachyon (such as one
in bosonic string theory), otherwise their new paper has nothing to say
about it.
__{_______________________________________________ _____________________________}
E-mail: lumo@matfyz.cz fax: +1-617/496-0110 Web: http://lumo.matfyz.cz/
eFax: +1-801/454-1858 work: +1-617/384-9488 home: +1-617/868-4487 (call)
Webs: http://schwinger.harvard.edu/~motl/ http://motls.blogspot.com/
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Lubos Motl
Feb3-05, 11:36 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 Thu, 3 Feb 2005, R.X. wrote:\n\n> I wouldn\'t see why such a decay would be energetically possible -\n> where are the tachyons in CY compactifications ?\n\nI am not really thinking about the detailed work by Allan et al. where the\ndecay is perturbative, but about a generalized "Witten bubble". Yes, I\ndon\'t see right now how to identify the analogue of the "Scherk-Schwarz\ncircle" or its higher-dimensional analogue that could lead to such\ninstabilities.\n\n> Ordinary CY compactifications tend to have supersymmetric vacuum\n> states with energy zero, so why should anything decay ?\n\nSure. These CY compactifications are also phenomenologically\nuninteresting. The realistic vacua are dS vacua obtained by adding\nsomething to the original SUSY vacuum - like those KKLT anti-D3-branes -\nand such additions may destabilize the background even under topology\nchange, unless you have a proof that it can\'t occur.\n\n> And BTW, it is known that all CY\'s are connected by extremal\n> transitions and so are (non-perturbatively) continuously connected -\n> no need to talk about tachyons here.\n\nRight. Incidentally, is it excluded that a conifold-like transition could\nsplit a Calabi-Yau into pieces? It\'s probably a trivial question, and the\nanswer is probably that it can\'t happen. Can someone tell me why?\n____________________________________________ __________________________________\nE-mail: lumo@matfyz.cz fax: +1-617/496-0110 Web: http://lumo.matfyz.cz/\neFax: +1-801/454-1858 work: +1-617/384-9488 home: +1-617/868-4487 (call)\nWebs: http://schwinger.harvard.edu/~motl/ http://motls.blogspot.com/\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 Thu, 3 Feb 2005, R.X. wrote:
> I wouldn't see why such a decay would be energetically possible -
> where are the tachyons in CY compactifications ?
I am not really thinking about the detailed work by Allan et al. where the
decay is perturbative, but about a generalized "Witten bubble". Yes, I
don't see right now how to identify the analogue of the "Scherk-Schwarz
circle" or its higher-dimensional analogue that could lead to such
instabilities.
> Ordinary CY compactifications tend to have supersymmetric vacuum
> states with energy zero, so why should anything decay ?
Sure. These CY compactifications are also phenomenologically
uninteresting. The realistic vacua are dS vacua obtained by adding
something to the original SUSY vacuum - like those KKLT anti-D3-branes -
and such additions may destabilize the background even under topology
change, unless you have a proof that it can't occur.
> And BTW, it is known that all CY's are connected by extremal
> transitions and so are (non-perturbatively) continuously connected -
> no need to talk about tachyons here.
Right. Incidentally, is it excluded that a conifold-like transition could
split a Calabi-Yau into pieces? It's probably a trivial question, and the
answer is probably that it can't happen. Can someone tell me why?
__{_______________________________________________ _____________________________}
E-mail: lumo@matfyz.cz fax: +1-617/496-0110 Web: http://lumo.matfyz.cz/
eFax: +1-801/454-1858 work: +1-617/384-9488 home: +1-617/868-4487 (call)
Webs: http://schwinger.harvard.edu/~motl/ http://motls.blogspot.com/
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Volker Braun
Feb3-05, 05:12 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 Thu, 03 Feb 2005 12:36:47 -0500, Lubos Motl wrote:\n\n> On Thu, 3 Feb 2005, R.X. wrote:\n>> And BTW, it is known that all CY\'s are connected by extremal\n>> transitions and so are (non-perturbatively) continuously connected\n\nI\'d agree if you would replace "known" by "believed". Or did I miss the\nproof?\n\n> Incidentally, is it excluded that a conifold-like transition could\n> split a Calabi-Yau into pieces? It\'s probably a trivial question, and the\n> answer is probably that it can\'t happen. Can someone tell me why?\n\nBy definition, an extremal transition is a blow down, followed by\ndeformation of the singularity. The blow down preserves connectedness. The\ndeformation (on a complex threefold) is surgery in (real) codimension\nthree, hence preserves connectedness. Only surgery in codimension one can\nsplit a manifold in two.\n\n-Volker\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 Thu, 03 Feb 2005 12:36:47 -0500, Lubos Motl wrote:
> On Thu, 3 Feb 2005, R.X. wrote:
>> And BTW, it is known that all CY's are connected by extremal
>> transitions and so are (non-perturbatively) continuously connected
I'd agree if you would replace "known" by "believed". Or did I miss the
proof?
> Incidentally, is it excluded that a conifold-like transition could
> split a Calabi-Yau into pieces? It's probably a trivial question, and the
> answer is probably that it can't happen. Can someone tell me why?
By definition, an extremal transition is a blow down, followed by
deformation of the singularity. The blow down preserves connectedness. The
deformation (on a complex threefold) is surgery in (real) codimension
three, hence preserves connectedness. Only surgery in codimension one can
split a manifold in two.
-Volker
Aaron Bergman
Feb4-05, 05:21 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>In article <pan.2005.02.03.23.05.00.380850-100000@physik.hu-berlin.de>,\nVolker Braun <volker.braun@physik.hu-berlin.de> wrote:\n\n> On Thu, 03 Feb 2005 12:36:47 -0500, Lubos Motl wrote:\n>\n> > On Thu, 3 Feb 2005, R.X. wrote:\n> >> And BTW, it is known that all CY\'s are connected by extremal\n> >> transitions and so are (non-perturbatively) continuously connected\n>\n> I\'d agree if you would replace "known" by "believed". Or did I miss the\n> proof?\n\nHas it even been proven for hypersurfaces in toric varieties, much less\ncomplete intersections?\n\nAaron\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>In article <pan.2005.02.03.23.05.00.380850-100000@physik.hu-berlin.de>,
Volker Braun <volker.braun@physik.hu-berlin.de> wrote:
> On Thu, 03 Feb 2005 12:36:47 -0500, Lubos Motl wrote:
>
> > On Thu, 3 Feb 2005, R.X. wrote:
> >> And BTW, it is known that all CY's are connected by extremal
> >> transitions and so are (non-perturbatively) continuously connected
>
> I'd agree if you would replace "known" by "believed". Or did I miss the
> proof?
Has it even been proven for hypersurfaces in toric varieties, much less
complete intersections?
Aaron
<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><\nI\'d agree if you would replace "known" by "believed". Or did I miss the\n\nproof?\n>\n\nHi Volker,\n\nthere are very strong indications for that. Of course, since the\nspace of all CY\'s is (to my knowledge) not known, one cannot say\nmuch definite about that, but the statement is true essentially for\nall the "known" classes of CY\'s like for example, complete intersection\nCICY\'s. For details, see eg: http://arXiv.org/abs/hep-th/9511230\n\n-W\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><
I'd agree if you would replace "known" by "believed". Or did I miss the
proof?
>
Hi Volker,
there are very strong indications for that. Of course, since the
space of all CY's is (to my knowledge) not known, one cannot say
much definite about that, but the statement is true essentially for
all the "known" classes of CY's like for example, complete intersection
CICY's. For details, see eg: http://arXiv.org/abs/http://www.arxiv.org/abs/hep-th/9511230
-W
Volker Braun
Feb4-05, 08:13 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>Hi W.,\n\nOn Fri, 04 Feb 2005 06:34:30 -0500, R.X. wrote:\n> [...] the statement is true essentially\n> for all the "known" classes of CY\'s like for example, complete\n> intersection CICY\'s.\n\nI would not be too surprised if it works for complete intersections in\ntoric varieties, but I tend to think that these are special. If you\nleave the realm of complete intersections very little is known (please\ncorrect :-). For example, take the Beauville manifold, is it connected to\nany other known CY threefold?\n\n-Volker\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>Hi W.,
On Fri, 04 Feb 2005 06:34:30 -0500, R.X. wrote:
> [...] the statement is true essentially
> for all the "known" classes of CY's like for example, complete
> intersection CICY's.
I would not be too surprised if it works for complete intersections in
toric varieties, but I tend to think that these are special. If you
leave the realm of complete intersections very little is known (please
correct :-). For example, take the Beauville manifold, is it connected to
any other known CY threefold?
-Volker
<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>To split a CY dynamically, the first question is to identify moduli\nwhere it \'splits\'. The definition for this should be that physical\nmodes propagating in two different regions decouple.\n\n> Only surgery in codimension one can split a manifold in two.\n\nDoes it matter how this looks geometrically for example what the\ndimension of the \'intermediate tube\' is ? At first sight no. At second\nthought one needs a barrier that prevents the gravity modes of\ndecaying into the tube and a low dimension of the tube might be\nhelpful, but neither necessary nor sufficient.\n\n> I still believe that similar kinds of topology changing transitions may\n> eventually destabilize or eliminate most of the "landscape". If you start\n> with a too convoluted Calabi-Yau space with fluxes, there will be many\n> modes how it can decay - it is potentially able to split into two (or\n> more) Calabi-Yau pieces.\n\nFirst, why should we consider a splitting within CY moduli spaces at\nall ? Adding potentials, does not preserve the CY concept, that is the\nsolution of EOM may be at a non CY metric. If for some reason we stick\nto CY, I don\'t see why a generic flux should drive the geometry to\nspecial \'split\' moduli in the CY, as compared to a generic point in the\ninterior of the moduli. It does not matter how \'convoluted\' the\nbackground is. In addition a \'split\' configuration would be almost\nwith certainty at infinite distance, at least in the usual metric. One\nwould then need an extra effect that renders the distance finite in the\nphysical metric.\n\nI am not saying that topology changes are unlikely, but I guess one\nneeds a framework beyond a \'decay of convoluted CY spaces into CY\npieces\' and probably new math.\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>To split a CY dynamically, the first question is to identify moduli
where it 'splits'. The definition for this should be that physical
modes propagating in two different regions decouple.
> Only surgery in codimension one can split a manifold in two.
Does it matter how this looks geometrically for example what the
dimension of the 'intermediate tube' is ? At first sight no. At second
thought one needs a barrier that prevents the gravity modes of
decaying into the tube and a low dimension of the tube might be
helpful, but neither necessary nor sufficient.
> I still believe that similar kinds of topology changing transitions may
> eventually destabilize or eliminate most of the "landscape". If you start
> with a too convoluted Calabi-Yau space with fluxes, there will be many
> modes how it can decay - it is potentially able to split into two (or
> more) Calabi-Yau pieces.
First, why should we consider a splitting within CY moduli spaces at
all ? Adding potentials, does not preserve the CY concept, that is the
solution of EOM may be at a non CY metric. If for some reason we stick
to CY, I don't see why a generic flux should drive the geometry to
special 'split' moduli in the CY, as compared to a generic point in the
interior of the moduli. It does not matter how 'convoluted' the
background is. In addition a 'split' configuration would be almost
with certainty at infinite distance, at least in the usual metric. One
would then need an extra effect that renders the distance finite in the
physical metric.
I am not saying that topology changes are unlikely, but I guess one
needs a framework beyond a 'decay of convoluted CY spaces into CY
pieces' and probably new math.
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