View Full Version : not surprised about the graviton?
Alejandro
Jul28-04, 01:48 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>Some days ago, in another forum, Urs wondered why some of us are very\npositive about the relationship between strings and gauge theory but\nwe are not excited about the point of strings "knowing gravity".\n\n[Moderator\'s note: I thought that Edward Witten experienced the strongest\nintellectual thrill in his life when he learned how string theory\npredicts gravity, and Witten is not the only one. ;-) LM]\n\nYep, if one thinks about it, it is surprising that I am not surprised.\nPerhaps it is because string lessons do not derive, as far as I have\nread, Einstein-Hilbert 4-dim action in some limit.\n\n[Moderator\'s note: Good textbooks and lectures of string theory - e.g.\nchapters 3 of Green+Schwarz+Witten and of Polchinski - derive that\nthe background metric must satisfy the correct Einstein equations if\nthe worldsheet theory is conformal i.e. consistent. They also explain\nthat the same effective action is seen by the scattering of the\nperturbations - namely by the gravitons. This is such a basic feature\nof string theory - and a key motivation to study it - that I would say\nthat someone who has not done/seen this calculation does not really know\nwhat string theory is at the technical level. LM]\n\nMost teachers just show a sort of consistent spin two particle and they\nsay "see, the graviton here". Some others note that string is about\nword-sheet actions, thus it contains a constant having the dimensions\nappropiate to measure curvature. But neither spin two nor curvature or\narea are definitive signatures of our gravity. It is possible to formulate\na curvature theory for other approximations to Einstein gravity, for\ninstance for Newtonian graviry.\n\n[Moderator\'s note: One can show the correct mass (zero), correct spin\n(two) and correct interactions of the graviton in string theory.\nMoreover, the correct interactions at low energies are guaranteed by\nthe consistency of the theory - general relativity is the only way how\nto define consistent nonzero couplings of massless spin two particles\nin a (special) relativistic theory. Because string theory defined as\na worldsheet theory can be shown to give a consistent spacetime theory,\nthe spacetime theory must automatically contain the right interactions\nat long distances, and explicit calculations show that this is indeed the\ncase. LM]\n\nPerhaps related to this doubt, note that also Electroweak Theory has a\nnon-renormalisable, area-like, constant: fermi constant. But it does\nnot have spin two particles by itself.\n\n[Moderator\'s note: Why should the electroweak theory have spin two\nparticles? LM]\n\nAnd one could devise some ways\nto formulate EW theory, or even electromagnetism, as a worldsheet\naction theory, thus sort of strings.\n\n[Moderator\'s note: Certainly not as anything analogous to string theory as\nwe know it. String theory, in the conventional meaning of the word,\nalways automatically includes gravity, and it is unique - once the five\ndifferent perturbative versions are unified. The idea that one can make\na consistent string theory that gives "electroweak theory only" is\na misunderstanding of basics of string theory. What sort of "new" string\ntheory do you have in mind? I think that this is a very popular laymen\'s\nmisunderstanding - they often think that it is possible to modify string\ntheory in hundreds of ways and define hundreds of different sibblings of\nstring theory. No, string theory - or a theory of quantum gravity -\nis unique. LM]\n\nBut I do not see how a elementary spin two field would be forced by using\nthese formulations.\n\n[Moderator\'s note: An elementary spin two field is described by a tensor\nwith at least two indices, say g_{mn}. Some of the components of this\ntensor would lead to negative-norm states - namely the mixed time-space\ncomponents. There must be a gauge symmetry that removes these unphysical\npolarizations and (linearized or nonlinear) general covariance is the\nonly possible gauge symmetry that can remove these states, and still lead\nto nonzero interactions. Just try to find a different solution, and you\nwill see that you fail. LM]\n\nAlejandro\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>Some days ago, in another forum, Urs wondered why some of us are very
positive about the relationship between strings and gauge theory but
we are not excited about the point of strings "knowing gravity".
[Moderator's note: I thought that Edward Witten experienced the strongest
intellectual thrill in his life when he learned how string theory
predicts gravity, and Witten is not the only one. ;-) LM]
Yep, if one thinks about it, it is surprising that I am not surprised.
Perhaps it is because string lessons do not derive, as far as I have
read, Einstein-Hilbert 4-dim action in some limit.
[Moderator's note: Good textbooks and lectures of string theory - e.g.
chapters 3 of Green+Schwarz+Witten and of Polchinski - derive that
the background metric must satisfy the correct Einstein equations if
the worldsheet theory is conformal i.e. consistent. They also explain
that the same effective action is seen by the scattering of the
perturbations - namely by the gravitons. This is such a basic feature
of string theory - and a key motivation to study it - that I would say
that someone who has not done/seen this calculation does not really know
what string theory is at the technical level. LM]
Most teachers just show a sort of consistent spin two particle and they
say "see, the graviton here". Some others note that string is about
word-sheet actions, thus it contains a constant having the dimensions
appropiate to measure curvature. But neither spin two nor curvature or
area are definitive signatures of our gravity. It is possible to formulate
a curvature theory for other approximations to Einstein gravity, for
instance for Newtonian graviry.
[Moderator's note: One can show the correct mass (zero), correct spin
(two) and correct interactions of the graviton in string theory.
Moreover, the correct interactions at low energies are guaranteed by
the consistency of the theory - general relativity is the only way how
to define consistent nonzero couplings of massless spin two particles
in a (special) relativistic theory. Because string theory defined as
a worldsheet theory can be shown to give a consistent spacetime theory,
the spacetime theory must automatically contain the right interactions
at long distances, and explicit calculations show that this is indeed the
case. LM]
Perhaps related to this doubt, note that also Electroweak Theory has a
non-renormalisable, area-like, constant: fermi constant. But it does
not have spin two particles by itself.
[Moderator's note: Why should the electroweak theory have spin two
particles? LM]
And one could devise some ways
to formulate EW theory, or even electromagnetism, as a worldsheet
action theory, thus sort of strings.
[Moderator's note: Certainly not as anything analogous to string theory as
we know it. String theory, in the conventional meaning of the word,
always automatically includes gravity, and it is unique - once the five
different perturbative versions are unified. The idea that one can make
a consistent string theory that gives "electroweak theory only" is
a misunderstanding of basics of string theory. What sort of "new" string
theory do you have in mind? I think that this is a very popular laymen's
misunderstanding - they often think that it is possible to modify string
theory in hundreds of ways and define hundreds of different sibblings of
string theory. No, string theory - or a theory of quantum gravity -
is unique. LM]
But I do not see how a elementary spin two field would be forced by using
these formulations.
[Moderator's note: An elementary spin two field is described by a tensor
with at least two indices, say g_{mn}. Some of the components of this
tensor would lead to negative-norm states - namely the mixed time-space
components. There must be a gauge symmetry that removes these unphysical
polarizations and (linearized or nonlinear) general covariance is the
only possible gauge symmetry that can remove these states, and still lead
to nonzero interactions. Just try to find a different solution, and you
will see that you fail. LM]
Alejandro
Alejandro
Aug1-04, 11:06 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>>> Yep, if one thinks about it, it is surprising that I am not surprised.\n>> Perhaps it is because string lessons do not derive, as far as I have\n>> read, Einstein-Hilbert 4-dim action in some limit.\n>\n> [Moderator\'s note: Good textbooks and lectures of string theory - e.g.\n> chapters 3 of Green+Schwarz+Witten and of Polchinski - derive that\n> the background metric must satisfy the correct Einstein equations if\n> the worldsheet theory is conformal i.e. consistent. They also explain\n\nAnd then do we have any proof that a solution of Einstein equations\nin 11 dimensions induces a solution of 4D equations in\nsome 4D submanifold? Sorry if my question is trivial, but I just would\nlike to be sure.\n\n[Moderator\'s note: A geometry of the form "M x K" with both factors being\nRicci-flat is Ricci-flat, too. It therefore satisfies Einstein\'s vacuum\nequations, too. In more general geometries, one must take the 10- or\n11-dimensional physics into account and the discussion would have to be\ncomplexified. LM]\n\n>> Most teachers just show a sort of consistent spin two particle and they\n>> say "see, the graviton here". Some others note that string is about\n>> word-sheet actions, thus it contains a constant having the dimensions\n>> appropiate to measure curvature. But neither spin two nor curvature or\n>> area are definitive signatures of our gravity. It is possible to formulate\n>> a curvature theory for other approximations to Einstein gravity, for\n>> instance for Newtonian graviry.\n>\n> [Moderator\'s note: One can show the correct mass (zero), correct spin\n> (two) and correct interactions of the graviton in string theory.\n\nTrue, but in the long long bibliography of string theory, is there some\npaper deriving a clasical gravitational wave from it? I mean, in the\nlimit h->0, or in the classical limit, or via some other standard\nmethod of dequantisation. The classical limit of QED can be done,\nor at least understood. Can we say the same about the classical limit\nof the stringy graviton?\n\n[Moderator\'s note: Yes, the classical wave, in the classical limit - more\nprecisely G_N goes to zero, *is* the graviton. The procedure works the\nother way around. You start with GR, linearize it, and see that a\ngravitational wave is a coherent state of massless spin 2 particles with\nthe right interactions, and this is what you find in string theory. This\nmeans that you can run these graviton backwards and find that they agree\nwith everything desirable in GR. Once you understand Chapters 3 of the\ntextbooks, all these extra questions are trivial indeed. LM]\n\nAlejandro\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>>> Yep, if one thinks about it, it is surprising that I am not surprised.
>> Perhaps it is because string lessons do not derive, as far as I have
>> read, Einstein-Hilbert 4-dim action in some limit.
>
> [Moderator's note: Good textbooks and lectures of string theory - e.g.
> chapters 3 of Green+Schwarz+Witten and of Polchinski - derive that
> the background metric must satisfy the correct Einstein equations if
> the worldsheet theory is conformal i.e. consistent. They also explain
And then do we have any proof that a solution of Einstein equations
in 11 dimensions induces a solution of 4D equations in
some 4D submanifold? Sorry if my question is trivial, but I just would
like to be sure.
[Moderator's note: A geometry of the form "M x K" with both factors being
Ricci-flat is Ricci-flat, too. It therefore satisfies Einstein's vacuum
equations, too. In more general geometries, one must take the 10- or
11-dimensional physics into account and the discussion would have to be
complexified. LM]
>> Most teachers just show a sort of consistent spin two particle and they
>> say "see, the graviton here". Some others note that string is about
>> word-sheet actions, thus it contains a constant having the dimensions
>> appropiate to measure curvature. But neither spin two nor curvature or
>> area are definitive signatures of our gravity. It is possible to formulate
>> a curvature theory for other approximations to Einstein gravity, for
>> instance for Newtonian graviry.
>
> [Moderator's note: One can show the correct mass (zero), correct spin
> (two) and correct interactions of the graviton in string theory.
True, but in the long long bibliography of string theory, is there some
paper deriving a clasical gravitational wave from it? I mean, in the
limit h->0, or in the classical limit, or via some other standard
method of dequantisation. The classical limit of QED can be done,
or at least understood. Can we say the same about the classical limit
of the stringy graviton?
[Moderator's note: Yes, the classical wave, in the classical limit - more
precisely G_N goes to zero, *is* the graviton. The procedure works the
other way around. You start with GR, linearize it, and see that a
gravitational wave is a coherent state of massless spin 2 particles with
the right interactions, and this is what you find in string theory. This
means that you can run these graviton backwards and find that they agree
with everything desirable in GR. Once you understand Chapters 3 of the
textbooks, all these extra questions are trivial indeed. LM]
Alejandro
Alejandro
Aug3-04, 12:52 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>> And then do we have any proof that a solution of Einstein equations\n> in 11 dimensions induces a solution of 4D equations in\n> some 4D submanifold? Sorry if my question is trivial, but I just would\n> like to be sure.\n>\n> [Moderator\'s note: A geometry of the form "M x K" with both factors being\n> Ricci-flat is Ricci-flat, too. It therefore satisfies Einstein\'s vacuum\n\nIs the inverse true? I mean, if a geometry in "MxK" is Ricci-flat,\ndoes it induce a Ricci-flat geometry in the two factors M and K?\nProbably yes, but I am not 100% sure now.\n\n> equations, too. In more general geometries, one must take the 10- or\n> 11-dimensional physics into account and the discussion would have to be\n> complexified. LM]\n\n\n> [Moderator\'s note: Yes, the classical wave, in the classical limit - more\n> precisely G_N goes to zero, *is* the graviton. The procedure works the\n> other way around. You start with GR, linearize it, and see that a\n> gravitational wave is a coherent state of massless spin 2 particles with\n> the right interactions, and this is what you find in string theory. This\n> means that you can run these graviton backwards and find that they agree\n> with everything desirable in GR. Once you understand Chapters 3 of the\n> textbooks, all these extra questions are trivial indeed. LM]\n\nYep, Weinberg used the linealization explanation already time ago in\nits gravitation book. Ok LM, you have convinced me, I will get the two\nbooks tomorrow. G_N tp zero does not seem a very usual classical\nlimit, but I will reserve my oppinion until I have read it.\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>> And then do we have any proof that a solution of Einstein equations
> in 11 dimensions induces a solution of 4D equations in
> some 4D submanifold? Sorry if my question is trivial, but I just would
> like to be sure.
>
> [Moderator's note: A geometry of the form "M x K" with both factors being
> Ricci-flat is Ricci-flat, too. It therefore satisfies Einstein's vacuum
Is the inverse true? I mean, if a geometry in "MxK" is Ricci-flat,
does it induce a Ricci-flat geometry in the two factors M and K?
Probably yes, but I am not 100% sure now.
> equations, too. In more general geometries, one must take the 10- or
> 11-dimensional physics into account and the discussion would have to be
> complexified. LM]
> [Moderator's note: Yes, the classical wave, in the classical limit - more
> precisely G_N goes to zero, *is* the graviton. The procedure works the
> other way around. You start with GR, linearize it, and see that a
> gravitational wave is a coherent state of massless spin 2 particles with
> the right interactions, and this is what you find in string theory. This
> means that you can run these graviton backwards and find that they agree
> with everything desirable in GR. Once you understand Chapters 3 of the
> textbooks, all these extra questions are trivial indeed. LM]
Yep, Weinberg used the linealization explanation already time ago in
its gravitation book. Ok LM, you have convinced me, I will get the two
books tomorrow. G_N tp zero does not seem a very usual classical
limit, but I will reserve my oppinion until I have read it.
Alejandro
Aug4-04, 12:40 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>Alejandro <arivero@posta.unizar.es> wrote in message news:<1d8a7d98.0408011159.a3bd56c-100000@posting.google.com>...\n\n> > [Moderator\'s note: Good textbooks and lectures of string theory - e.g.\n> > chapters 3 of Green+Schwarz+Witten and of Polchinski - derive that\n> > the background metric must satisfy the correct Einstein equations if\n> > the worldsheet theory is conformal i.e. consistent.\n\nPerhaps the language generated some of my doubts. Polchinski, pg. 112.\njust says "The equation b... resembles Einstein\'s equation". The word\n"resembles" sounds far away from a theorem. It implies that the author is\nbeing cautious about having gravity there.\n\n[Moderator\'s note: Nope. You misunderstood the word "resembles". The\nreason why Polchinski uses the word "resembles" is surely not his\nuncertainty about whether string theory contains gravity. There is no\nroom for such an uncertainty and such doubts. The verb "resemble"\nmeans "look like" - in other words, the equations that one derives\nare not exactly the original Einstein\'s equations, but Einstein\'s\nequations coupled to matter (dilaton, B-field...) which also can\nacquire various new alpha\' corrections. String theory also implies\nwhat sort of matter and corrections appear, and this implication\nis rigorous. The word "resemble" means that the equations are not\nquite the pure and simple laws of GR from 1915. But this disagreement\ndoes not show a flaw of string theory; on the contrary, it shows\nthat the simple laws of GR were not the whole story. LM]\n\nHmm. Do you remember where in the books is the limit of small Newton\nconstant?\n\n[Moderator\'s note: which limit you exactly want? Linearized gravity?\nIn perturbative string theory, GR is obtained in the limit alpha\' goes\nto zero - in other words, at distances much longer than l_{string},\nthe typical length scale associated with strings. Newton\'s constant\nis a power of alpha\' - determined by dimensional analysis - times\ng_{string}^2. Sending g_{string} to zero is not enough to reduce string\ntheory to pure GR. Even at vanishing string coupling - or, perhaps,\nespecially at vanishing string coupling - string theory differs from\nGR or any other theory of pointlike particles. The stringy equations\nof motion - for the background - are derived in Polchinski. The whole\nproof is there and everyone who knows how to take limits can take them.\nI am not sure what you\'re exactly looking for. But if you want to derive\nthe Newtonian limit of GR, the same proof from GR can be used in string\ntheory as well, as long as the distances between all objects are much\nlonger than l_{string} where GR is a good approximation of the full\n(string) theory. LM]\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>Alejandro <arivero@posta.unizar.es> wrote in message news:<1d8a7d98.0408011159.a3bd56c-100000@posting.google.com>...
> > [Moderator's note: Good textbooks and lectures of string theory - e.g.
> > chapters 3 of Green+Schwarz+Witten and of Polchinski - derive that
> > the background metric must satisfy the correct Einstein equations if
> > the worldsheet theory is conformal i.e. consistent.
Perhaps the language generated some of my doubts. Polchinski, pg. 112.
just says "The equation b... resembles Einstein's equation". The word
"resembles" sounds far away from a theorem. It implies that the author is
being cautious about having gravity there.
[Moderator's note: Nope. You misunderstood the word "resembles". The
reason why Polchinski uses the word "resembles" is surely not his
uncertainty about whether string theory contains gravity. There is no
room for such an uncertainty and such doubts. The verb "resemble"
means "look like" - in other words, the equations that one derives
are not exactly the original Einstein's equations, but Einstein's
equations coupled to matter (dilaton, B-field...) which also can
acquire various new \alpha' corrections. String theory also implies
what sort of matter and corrections appear, and this implication
is rigorous. The word "resemble" means that the equations are not
quite the pure and simple laws of GR from 1915. But this disagreement
does not show a flaw of string theory; on the contrary, it shows
that the simple laws of GR were not the whole story. LM]
Hmm. Do you remember where in the books is the limit of small Newton
constant?
[Moderator's note: which limit you exactly want? Linearized gravity?
In perturbative string theory, GR is obtained in the limit \alpha' goes
to zero - in other words, at distances much longer than l_{string},
the typical length scale associated with strings. Newton's constant
is a power of \alpha' - determined by dimensional analysis - times
g_{string}^2. Sending g_{string} to zero is not enough to reduce string
theory to pure GR. Even at vanishing string coupling - or, perhaps,
especially at vanishing string coupling - string theory differs from
GR or any other theory of pointlike particles. The stringy equations
of motion - for the background - are derived in Polchinski. The whole
proof is there and everyone who knows how to take limits can take them.
I am not sure what you're exactly looking for. But if you want to derive
the Newtonian limit of GR, the same proof from GR can be used in string
theory as well, as long as the distances between all objects are much
longer than l_{string} where GR is a good approximation of the full
(string) theory. LM]
[Moderator's note: ...There is no
room for such an uncertainty and such doubts. The verb "resemble"
means "look like" - in other words, the equations that one derives
are not exactly the original Einstein's equations, but Einstein's
equations coupled to matter (dilaton, B-field...) which also can
acquire various new corrections]
I see. I also was understanding that it is exagerated to say from it that strings quantise general relativity. It seems that the precise claim is that
string theory is able to execute a consistent quantisation of Kaluza Klein theory when this theory has a definite critical dimension and a definite content of matter fields. This is seen as a virtue because of the uniqueness: it fixes a very specific family of theories, say 26 dim Kaluza Klein or, better, the 10 dim SUSY version, and a specific way to have matter inside. But the claim anyway is about Kaluza Klein theory, not about Einstein theory.
I am not surprised about having a measuring of background curvature from string theory. It is well known that the curvatures in Riemann tensor are essentially a set of two-dimensional objects, so it was to be expected that a two dimensional method as the string worldsheet were able to catch the tensor action.
>>Hmm. Do you remember where in the books is the limit of small Newton
>>constant?
[Moderator's note: which limit you exactly want? Linearized gravity?
...I am not sure what you're exactly looking for. But if you want to derive
the Newtonian limit of GR, the same proof from GR can be used in string
theory as well, as long as the distances between all objects are much
longer than where GR is a good approximation of the full
(string) theory. LM]
No, no need of newtonian gravity thanks (by the way, a friend did time ago a nice reelaboration of Feynman version of classical gravity, using curvatures all the time as in GR). I mentioned small G because you told about it, but I was really asking for a verification of the quantisation property. In
the same way that one can get classical electrodinamics from QED, one
should be able to get the classical Kaluza Klein theory in some
limit.
Sometimes the limit process is not the most naive; remember for instance how quantum mechanics approaches classical mechanics in the limit of high quantum numbers, not really in the h->0.
Well, I will be on vacation for some days, but I will carry the GSW in the
backpack (the Polchinski was not ready for loan). will surely to read news still tomorrow or past tomorrow.
Alejandro
Urs Schreiber
Aug12-04, 01:06 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, 7 Aug 2004, arivero wrote:\n\n> I am not surprised about having a measuring of background curvature\n> from string theory. It is well known that the curvatures in Riemann\n> tensor are essentially a set of two-dimensional objects, so it was to\n> be expected that a two dimensional method as the string worldsheet were\n> able to catch the tensor action.\n\nYou are not surprised about this?\n\nAs far as I understand you are roughly referring to the phenomenon that\nthe 2-dimensionality of the worldsheet is related to the fact that it can\ndescribe particles carrying 2 spacetime indices (since its spectrum is\ngenerated by two independent copies (left and rightmoving) of\noscillators).\n\nThat alone is easy to understand from elementary string quantization. But\nthat the resulting dynamics is describes by the Ricci tensor which _also_\nis rank 2 (which is vaguely related to the above appearence of the number\n2) is not all that obvious, a priori. (It is now, of course.)\n\n\n> No, no need of newtonian gravity thanks (by the way, a friend did time ago\n> a nice reelaboration of Feynman version of classical gravity, using\n> curvatures all the time as in GR). I mentioned small G because you told\n> about it, but I was really asking for a verification of the quantisation\n> property. In the same way that one can get classical electrodinamics from\n> QED, one should be able to get the classical Kaluza Klein theory in some\n> limit.\n\nYes, as Lubos has already indicated, that\'s no mystery at all. In the\nalpha\'->0 limit the effective field theory of strings is that of GR\n(sugra really). From that point on you can do with this standard sugra\naction whatever you want to do in field theory.\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, 7 Aug 2004, arivero wrote:
> I am not surprised about having a measuring of background curvature
> from string theory. It is well known that the curvatures in Riemann
> tensor are essentially a set of two-dimensional objects, so it was to
> be expected that a two dimensional method as the string worldsheet were
> able to catch the tensor action.
You are not surprised about this?
As far as I understand you are roughly referring to the phenomenon that
the 2-dimensionality of the worldsheet is related to the fact that it can
describe particles carrying 2 spacetime indices (since its spectrum is
generated by two independent copies (left and rightmoving) of
oscillators).
That alone is easy to understand from elementary string quantization. But
that the resulting dynamics is describes by the Ricci tensor which _also_
is rank 2 (which is vaguely related to the above appearence of the number
2) is not all that obvious, a priori. (It is now, of course.)
> No, no need of newtonian gravity thanks (by the way, a friend did time ago
> a nice reelaboration of Feynman version of classical gravity, using
> curvatures all the time as in GR). I mentioned small G because you told
> about it, but I was really asking for a verification of the quantisation
> property. In the same way that one can get classical electrodinamics from
> QED, one should be able to get the classical Kaluza Klein theory in some
> limit.
Yes, as Lubos has already indicated, that's no mystery at all. In the
\alpha'->0 limit the effective field theory of strings is that of GR
(sugra really). From that point on you can do with this standard sugra
action whatever you want to do in field theory.
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