string theory, general relativity, diffeomorphism invariance

Aug20-04, 06:42 AM

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','to olbar=no,location=no,scrollbars=yes,resizable=yes, status=no,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usene t 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>if string theory\'s graviton-graviton scattering has not been proven\nconsistent beyond 2-loops, then on a macroscopic scale, how do string\ntheorists know string theory reproduces general relativity on all\norders?\n\ndoes string theory obey diffeomorphism invariance (aka general\ncovariance) as an exact symmetry in nature, or does it break\ndiffeomorphism invariance? if it does break diffeomorphism\ninvariance, then is it correct to say string theory merges general\nrelativity with quantum field theory?\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>if string theory's graviton-graviton scattering has not been proven
consistent beyond 2-loops, then on a macroscopic scale, how do string
theorists know string theory reproduces general relativity on all
orders?

does string theory obey diffeomorphism invariance (aka general
covariance) as an exact symmetry in nature, or does it break
diffeomorphism invariance? if it does break diffeomorphism
invariance, then is it correct to say string theory merges general
relativity with quantum field theory?

Aug20-04, 01:31 PM

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','to olbar=no,location=no,scrollbars=yes,resizable=yes, status=no,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usene t 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>Daniel <ensabah6@yahoo.com> wrote in message news:<ba566c17.0408192104.1ad441dd-100000@posting.google.com>...\n> if string theory\'s graviton-graviton scattering has not been proven\n> consistent beyond 2-loops, then on a macroscopic scale, how do string\n> theorists know string theory reproduces general relativity on all\n> orders?\n>\n> does string theory obey diffeomorphism invariance (aka general\n> covariance) as an exact symmetry in nature, or does it break\n> diffeomorphism invariance? if it does break diffeomorphism\n> invariance, then is it correct to say string theory merges general\n> relativity with quantum field theory?\n\nStrings can propagate consistently only in backgrounds that satisfy\nappropriate field equations. One of these equations resembles\nEinstein\'s equation with source terms from an antisymmetric tensor\nfield and the dilaton.\n\nTo be more specific, the essential requirement that physics cannot\ndepend on what coordinates are chosen to parameterize the worldsheet,\nis equivalent in the Polyakov approach to the requirement of\ndiffeomorphism and Weyl invariance of the 2 dimensional worldsheet\nquantum field theory. Expanding the anomalous Weyl transformation of\nthe target space metric to order \\$\\alpha\'\\$ and requiring that it\nvanishes -- as you must to preserve consistency -- gives you the\nEinstein like equation I mentioned. The diffeomorphism times Weyl\ninvariance of the 2 dimensional worldsheet theory is exact by\nrequirement of consistency.\n\nYou do expect (and get) additional corrections to Einstein\'s equation\nat order \\$\\alpha\'^2\\$ and beyond. The claim is that string theory is a\nconsistent quantum theory that necessarily includes gravity. I do not\nthink anyone serious claims that it reproduces four dimensional\nclassical general relativity to all orders.\n\nAs to your second point, the graviton-graviton scattering: It is true\nthat our current understanding of this process is very limited. If you\ntry to do this in a region of moduli space where the string theory is\nweakly coupled (g<<1), the relevant coupling for graviton-graviton\nscattering is still strong and string perturbation theory has broken\ndown. That is, each term in the expansion is larger than the one\nbefore and by calculating such terms in turn you learn nothing. To\novercome this difficulty, it is likely that we need to gain more\nconceptual insight into the dynamics of the theory. Hopefully a\nnonperturbative approach such as M-theory can help to make progress in\nthis direction.\n\nBut let me be very clear: These difficulties do not interfere by any\nmeans with the point made above about Einstein\'s equation. You do not\nneed to understand how to calculate graviton-graviton scattering in\norder to see that string theory is a consistent theory of quantum\ngravity. (Of course, that is not to say that it would not be highly\ndesirable to understand that process.)\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>Daniel <ensabah6@yahoo.com> wrote in message news:<ba566c17.0408192104.1ad441dd-1...google.com>...
> if string theory's graviton-graviton scattering has not been proven
> consistent beyond 2-loops, then on a macroscopic scale, how do string
> theorists know string theory reproduces general relativity on all
> orders?
>
> does string theory obey diffeomorphism invariance (aka general
> covariance) as an exact symmetry in nature, or does it break
> diffeomorphism invariance? if it does break diffeomorphism
> invariance, then is it correct to say string theory merges general
> relativity with quantum field theory?

Strings can propagate consistently only in backgrounds that satisfy
appropriate field equations. One of these equations resembles
Einstein's equation with source terms from an antisymmetric tensor
field and the dilaton.

To be more specific, the essential requirement that physics cannot
depend on what coordinates are chosen to parameterize the worldsheet,
is equivalent in the Polyakov approach to the requirement of
diffeomorphism and Weyl invariance of the 2 dimensional worldsheet
quantum field theory. Expanding the anomalous Weyl transformation of
the target space metric to order $LaTeX Code: $\\alphasingle-quote$$ and requiring that it
vanishes -- as you must to preserve consistency -- gives you the
Einstein like equation I mentioned. The diffeomorphism times Weyl
invariance of the 2 dimensional worldsheet theory is exact by
requirement of consistency.

You do expect (and get) additional corrections to Einstein's equation
at order $LaTeX Code: $\\alphasingle-quote^2$$ and beyond. The claim is that string theory is a
consistent quantum theory that necessarily includes gravity. I do not
think anyone serious claims that it reproduces four dimensional
classical general relativity to all orders.

As to your second point, the graviton-graviton scattering: It is true
that our current understanding of this process is very limited. If you
try to do this in a region of moduli space where the string theory is
weakly coupled (g<<1), the relevant coupling for graviton-graviton
scattering is still strong and string perturbation theory has broken
down. That is, each term in the expansion is larger than the one
before and by calculating such terms in turn you learn nothing. To
overcome this difficulty, it is likely that we need to gain more
conceptual insight into the dynamics of the theory. Hopefully a
nonperturbative approach such as M-theory can help to make progress in
this direction.

But let me be very clear: These difficulties do not interfere by any
means with the point made above about Einstein's equation. You do not
need to understand how to calculate graviton-graviton scattering in
order to see that string theory is a consistent theory of quantum
gravity. (Of course, that is not to say that it would not be highly
desirable to understand that process.)

Aug20-04, 01:47 PM

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','to olbar=no,location=no,scrollbars=yes,resizable=yes, status=no,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usene t 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 Fri, 20 Aug 2004, Daniel wrote:\n\n> if string theory\'s graviton-graviton scattering has not been proven\n> consistent beyond 2-loops, then on a macroscopic scale, how do string\n> theorists know string theory reproduces general relativity on all\n> orders?\n\nThis sentence contains several confusing points at different levels. The\nstatement about the possible inconsistency of multiloop amplitudes is a\nvery popular kind of poison distributed by certain people, especially from\nCanada, who don\'t really follow string theory well, but who have certain\npersonal interests to say bad things about it.\n\nThere exist physically satisfactory arguments why the string perturbative\nexpansion is finite order by order - to all orders and beyond - and there\nexist no viable ideas that would indicate that anything is wrong at the\nmultiloop level. Multiloop amplitudes require us to insert many picture\nchanging operators which is a technically complicated tool necessary for\nthe superstring.\n\nBut all these things can be done, and various things have been explicitly\nat the two loop level. There exist potentially better formalisms,\nespecially one by Nathan Berkovits based on pure spinors. See one of his\nrecent papers\n\nhttp://arxiv.org/abs/hep-th/0406055\n\nwhere he shows a procedure to calculate arbitrary multiloop amplitudes and\nwhere he proves certain critical vanishing theorems. What is important is\nthat string theory, regardless of the formulation we choose, is free of\nthe the UV (short distance) divergences. Technically it is because the\nloop amplitudes - one-loop as well as higher-loop amplitudes - are written\nas integrals over the moduli space of Riemann surfaces. These moduli\nspaces are essentially compact manifolds and all of their singular points\nor "boundaries" can be interpreted as limits of stringy diagrams\ndescribing *infrared* regime of point-like particle diagrams.\n\nEquivalently, the stringy diagrams can be rewritten as pointlike diagrams\nbut with the UV regions of the integrals removed essentially because of\nthe extended character of the string.\n\nIn other words, all potential divergences, even those that would look as\nUV divergences, can be reinterpreted as IR divergences, due to the\nstructure of the moduli space of shapes of the genus g diagrams. This fact\ncan be seen very easily for the torus - whose shape is parameterized by\nthe complex number "tau" and "tau" going to "i.infinity" describes the\nonly potentially divergent region of the "fundamental domain" of the\ntau-plane - the coset of the upper half-plane over the modular group\nSL(2,Z). But it is not hard to perform an analogous proof for higher\ngenera - the moduli spaces are not that complicated.\n\nThis step reduces the proof of finiteness to two remaining tasks: to show\nthat the integrand is finite for finite values of the moduli; and to show\nthat only the physically expected IR divergences exist in the asymptotic\nregions of the moduli space - the latter is a test about the low energy\nphysics.\n\nBe sure that these things can be done and they have been done well enough\nso that virtually no one is really interested in these problems anymore.\nMoreover, the unitarity of the resulting amplitudes at any order can\neasily be seen in the light cone gauge where it follows from the\nhermiticity of the Hamiltonian. The comments suggesting that a possible\ninconsistency of stringy multiloop amplitudes is something that string\ntheorists must worry about today, in 2004, or perhaps even one of the\nimportant problems facing string theory are absolutely unrealistic - I\nwould say that they are not true - and no one should believe this kind of\nbullshitting distributed by non-experts.\n\nThe cancellation of various unwanted IR divergences depends on certain\nvanishing theorems. For the case of the superstring it was always a bit\ncumbersome to write down the full formula including the correct picture\nchanging operators etc., but these technical problems can be overcome\ntoday.\n\nOK, a lower level of your confusion is that you say that string theory\nshould reproduce GR to all orders. That\'s certainly not the case. It would\nbe a disaster for a theory to reproduce GR beyond the tree-level or\none-loop level - simply because GR is inconsistent and non-renormalizable\nat two-loop level and beyond. It is the whole point of a quantum theory of\ngravity - also called string theory - that this better quantum theory must\nmake sense beyond the tree level. String theory achieves it.\nPerturbatively it is because a lot of new physics - and new terms in the\neffective action suppressed by powers of (\\alpha\')^2. Nonperturbatively we\nwould have to distinguish the string scale and the Planck scale and refine\nthe proofs - but at any rate, string theory (or any working quantum theory\nof gravity) predicts higher-order quantum corrections (with positive\npowers of \\hbar) that GR has no idea about. This is exactly why a new\ntheory is needed that goes beyond GR. The results of GR would be infinite.\n\nThe agreement is obtained with the low-energy limit of classical physics.\nClassical GR is a non-linear theory - the gravitons self-interact, so to\nsay - and all of this non-linear structure can be seen to follow from\nstring theory. (More precisely, it is always a certain extension with\nother massless fields - e.g. the B-field and the dilaton, as well as their\nfermionic superpartners - and perhaps some extra dimensions.)\n\n> does string theory obey diffeomorphism invariance (aka general\n> covariance) as an exact symmetry in nature, or does it break\n> diffeomorphism invariance?\n\nString theory reproduces all physical consequences that would follow from\ndiffeomorphism invariance, but all these consequences are guaranteed\n"automatically" by deeper rules of string theory. The diffeomorphism\ninvariance does not have to be required by hand; string theory is not just\nGR and the calculations are done differently in these two theories. The\nquestion "what is the local symmetry group of Nature" is not really\nwell-defined - the local symmetry group depends on the degrees of freedom\nthat we start with; the role of the local symmetry group is to remove some\ndegrees of freedom. The gauge group describes *redundancy* of our\ndescription. In general, there exist different equivalent starting points\nwith different gauge symmetries that nevertheless reproduce the same\nphysics - because of Seiberg dualities and S-dualities, holography, matrix\nmodels, higgsing, unhiggshing, and confinement, and other equivalences.\n\nMoreover, in string theory, the diffeomorphism invariance is just a tiny\npart of the whole symmetry group. This invariance is connected with the\ngraviton, one of the lowest-energy stringy vibrations. But there exist an\ninfinite tower of other stringy vibrational patterns, and more or less\neach of them is associated with a counterpart of general covariance. These\nnew symmetries - and the corresponding new physical phenomena - become\nrelevant especially at the very short distances comparable to l_{string}\nand shorter.\n\n> if it does break diffeomorphism invariance, then is it correct to say\n> string theory merges general relativity with quantum field theory?\n\nNo, it does not break diffeomorphism invariance in any physical way. The\nclassical & low energy results of GR are untouched. But once again, the\nhigh energy (very short distance) & quantum corrections cannot be\npredicted by GR, and this is why a better theory is needed. The only known\nsuch better theory is called string/M-theory.\n_________________________________________ _____________________________________\nE-mail: lumo@matfyz.cz fax: +1-617/496-0110 Web: http://lumo.matfyz.cz/\neFax: +1-801/454-1858 work: +1-617/496-8199 home: +1-617/868-4487 (call)\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 Fri, 20 Aug 2004, Daniel wrote:

> if string theory's graviton-graviton scattering has not been proven
> consistent beyond 2-loops, then on a macroscopic scale, how do string
> theorists know string theory reproduces general relativity on all
> orders?

This sentence contains several confusing points at different levels. The
statement about the possible inconsistency of multiloop amplitudes is a
very popular kind of poison distributed by certain people, especially from
Canada, who don't really follow string theory well, but who have certain
personal interests to say bad things about it.

There exist physically satisfactory arguments why the string perturbative
expansion is finite order by order - to all orders and beyond - and there
exist no viable ideas that would indicate that anything is wrong at the
multiloop level. Multiloop amplitudes require us to insert many picture
changing operators which is a technically complicated tool necessary for
the superstring.

But all these things can be done, and various things have been explicitly
at the two loop level. There exist potentially better formalisms,
especially one by Nathan Berkovits based on pure spinors. See one of his
recent papers

http://arxiv.org/abs/http://www.arxi...hep-th/0406055

where he shows a procedure to calculate arbitrary multiloop amplitudes and
where he proves certain critical vanishing theorems. What is important is
that string theory, regardless of the formulation we choose, is free of
the the UV (short distance) divergences. Technically it is because the
loop amplitudes - one-loop as well as higher-loop amplitudes - are written
as integrals over the moduli space of Riemann surfaces. These moduli
spaces are essentially compact manifolds and all of their singular points
or "boundaries" can be interpreted as limits of stringy diagrams
describing *infrared* regime of point-like particle diagrams.

Equivalently, the stringy diagrams can be rewritten as pointlike diagrams
but with the UV regions of the integrals removed essentially because of
the extended character of the string.

In other words, all potential divergences, even those that would look as
UV divergences, can be reinterpreted as IR divergences, due to the
structure of the moduli space of shapes of the genus g diagrams. This fact
can be seen very easily for the torus - whose shape is parameterized by
the complex number " $LaTeX Code: \\tau$ " and " $LaTeX Code: \\tau$ " going to "i.infinity" describes the
only potentially divergent region of the "fundamental domain" of the
$LaTeX Code: \\tau-plane -$ the coset of the upper half-plane over the modular group
SL(2,Z). But it is not hard to perform an analogous proof for higher
genera - the moduli spaces are not that complicated.

This step reduces the proof of finiteness to two remaining tasks: to show
that the integrand is finite for finite values of the moduli; and to show
that only the physically expected IR divergences exist in the asymptotic
regions of the moduli space - the latter is a test about the low energy
physics.

Be sure that these things can be done and they have been done well enough
so that virtually no one is really interested in these problems anymore.
Moreover, the unitarity of the resulting amplitudes at any order can
easily be seen in the light cone gauge where it follows from the
hermiticity of the Hamiltonian. The comments suggesting that a possible
inconsistency of stringy multiloop amplitudes is something that string
theorists must worry about today, in 2004, or perhaps even one of the
important problems facing string theory are absolutely unrealistic - I
would say that they are not true - and no one should believe this kind of
bullshitting distributed by non-experts.

The cancellation of various unwanted IR divergences depends on certain
vanishing theorems. For the case of the superstring it was always a bit
cumbersome to write down the full formula including the correct picture
changing operators etc., but these technical problems can be overcome
today.

OK, a lower level of your confusion is that you say that string theory
should reproduce GR to all orders. That's certainly not the case. It would
be a disaster for a theory to reproduce GR beyond the tree-level or
one-loop level - simply because GR is inconsistent and non-renormalizable
at two-loop level and beyond. It is the whole point of a quantum theory of
gravity - also called string theory - that this better quantum theory must
make sense beyond the tree level. String theory achieves it.
Perturbatively it is because a lot of new physics - and new terms in the
effective action suppressed by powers of $LaTeX Code: (\\alphasingle-quote)^2$ . Nonperturbatively we
would have to distinguish the string scale and the Planck scale and refine
the proofs - but at any rate, string theory (or any working quantum theory
of gravity) predicts higher-order quantum corrections (with positive
powers $LaTeX Code: of \\hbar)$ that GR has no idea about. This is exactly why a new
theory is needed that goes beyond GR. The results of GR would be infinite.

The agreement is obtained with the low-energy limit of classical physics.
Classical GR is a non-linear theory - the gravitons self-interact, so to
say - and all of this non-linear structure can be seen to follow from
string theory. (More precisely, it is always a certain extension with
other massless fields - e.g. the B-field and the dilaton, as well as their
fermionic superpartners - and perhaps some extra dimensions.)

> does string theory obey diffeomorphism invariance (aka general
> covariance) as an exact symmetry in nature, or does it break
> diffeomorphism invariance?

String theory reproduces all physical consequences that would follow from
diffeomorphism invariance, but all these consequences are guaranteed
"automatically" by deeper rules of string theory. The diffeomorphism
invariance does not have to be required by hand; string theory is not just
GR and the calculations are done differently in these two theories. The
question "what is the local symmetry group of Nature" is not really
well-defined - the local symmetry group depends on the degrees of freedom
that we start with; the role of the local symmetry group is to remove some
degrees of freedom. The gauge group describes *redundancy* of our
description. In general, there exist different equivalent starting points
with different gauge symmetries that nevertheless reproduce the same
physics - because of Seiberg dualities and S-dualities, holography, matrix
models, higgsing, unhiggshing, and confinement, and other equivalences.

Moreover, in string theory, the diffeomorphism invariance is just a tiny
part of the whole symmetry group. This invariance is connected with the
graviton, one of the lowest-energy stringy vibrations. But there exist an
infinite tower of other stringy vibrational patterns, and more or less
each of them is associated with a counterpart of general covariance. These
new symmetries - and the corresponding new physical phenomena - become
relevant especially at the very short distances comparable to $LaTeX Code: l_{string}$
and shorter.

> if it does break diffeomorphism invariance, then is it correct to say
> string theory merges general relativity with quantum field theory?

No, it does not break diffeomorphism invariance in any physical way. The
classical & low energy results of GR are untouched. But once again, the
high energy (very short distance) & quantum corrections cannot be
predicted by GR, and this is why a better theory is needed. The only known
such better theory is called string/M-theory.
__{_______________________________________________ _____________________________}
E-mail: lumo@matfyz.cz fax:

Web: http://lumo.matfyz.cz/
eFax:

work:

home:

(call)
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^

Aug21-04, 02:09 PM

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','to olbar=no,location=no,scrollbars=yes,resizable=yes, status=no,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usene t 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 Motl <motl@feynman.harvard.edu> wrote in message news:<Pine.LNX.4.31.0408201309540.3368-100000@einstein.physics.harvard.edu>...\n\nA few comments on:\n\n> Equivalently, the stringy diagrams can be rewritten as pointlike diagrams\n> but with the UV regions of the integrals removed essentially because of\n> the extended character of the string.\n>\nIt is a subtle but important point that string theory\namplitudes should not be interpreted/viewed as simple superposition\nof particle amplitudes with a cutoff. At one loop, one can see this\nby noting that the lower boundary of the fundamental domain is\ncurved and not a straight line. If it were straight, it would\namount to a projection on excitations that obey N_L=N_R (this\nprojection is in force on external legs which can be thought of as\nthin cylinders; that is, external particles must satisfy that\nwell-known condition, actually it is one of the conditions for\nphysical states).\n\nHowever since the lower boundary of the torus fundamental region\nis curved, string excitations that do _not_ satisfy N_L=N_R do\ncontribute in the loop. They generically contribute in any loop\n(with exceptions), and in a way precisely required by consistency\n(as encoded in the intricate geometry of the modular integration\ndomains). However such excitations which do not satisfy N_L=N_R\ndo in general not have a standard particle field theory interpretation !\n\nThis means that the intricate properties of string loops, and\nspecifically those which make they theory consistent, cannot be\ncaptured by summing naive particle QFT (well, that\'s not a theorem\nbut I think it is quite obvious). Even if you would start\nwith infinitely many particle excitations and put cutoffs as you\nplease, you would miss the knowledge of the extra contributions\nneeded to render the theory consistent, ie., you would lack the\nmodular geometry of riemann surfaces.\n\nThis had first been put into this context by Greg Moore in a beautiful\n(and IMHO underappreciated) paper in the mid-80\'s ("Atkin-Lehner\nsymmetry"), where it was demonstrated in an example that the tachyon\ncan make the dominant contribution in a heterotic string loop, despite\nthe fact that the tachyon is GSO-projected out and thus cannot appear\nas external particle.\n\n[The aim of that paper was to see whether one can get vanishing\nloop amplitudes (such as the vacuum energy) in non-supersymmetric\ntheories, as an effect of these "extra" contributions to loop\namplitudes; the idea was that in order for an amplitude to vanish,\nit it not necessary that the integrand dumbly vanishes term by term (as\nin a susy theory), but all what is necessary is that the modular\nintegral over it vanishes (which is obviously a weaker condition).]\n\nIn a nutshell, already perturbative string theory is much more than\nparticle quantum field theory (not to speak about non-pertubative\nproperties).\nIn view of this, one may ponder whether it is a good idea to\nuse particle QFT intuition for addressing questions like the\nvanishing of the vacuum energy or scalar self-energies, etc; but that\'s\nanother topic.\n\n\nAs far as the main question of the thread is concerned:\nLubos answered it at length, let me summarize it in two sentences:\n\nString theory does not predict GR (in the sense of Einstein\'s\nlagrangian) in the low energy effective action, but GR with infinitely\nmany corrections (eg higher powers in the curvature, which however\nplay no role at macroscopic scales). What string theory guarantees\nis general coordinate invariance of this effective action, and this\nas a consequence of the conformal symmetry of the world-sheet theory.\n\n-WL\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 Motl <motl@feynman.harvard.edu> wrote in message news:<Pine.LNX.4.31.0408201309540.33...arvard.edu>...

A few comments on:

> Equivalently, the stringy diagrams can be rewritten as pointlike diagrams
> but with the UV regions of the integrals removed essentially because of
> the extended character of the string.
>
It is a subtle but important point that string theory
amplitudes should not be interpreted/viewed as simple superposition
of particle amplitudes with a cutoff. At one loop, one can see this
by noting that the lower boundary of the fundamental domain is
curved and not a straight line. If it were straight, it would
amount to a projection on excitations that obey

(this
projection is in force on external legs which can be thought of as
thin cylinders; that is, external particles must satisfy that
well-known condition, actually it is one of the conditions for
physical states).

However since the lower boundary of the torus fundamental region
is curved, string excitations that

satisfy

do
contribute in the loop. They generically contribute in any loop
(with exceptions), and in a way precisely required by consistency
(as encoded in the intricate geometry of the modular integration
domains). However such excitations which do not satisfy

do in general not have a standard particle field theory interpretation !

This means that the intricate properties of string loops, and
specifically those which make they theory consistent, cannot be
captured by summing naive particle QFT (well, that's not a theorem
but I think it is quite obvious). Even if you would start
with infinitely many particle excitations and put cutoffs as you
please, you would miss the knowledge of the extra contributions
needed to render the theory consistent, ie., you would lack the
modular geometry of riemann surfaces.

This had first been put into this context by Greg Moore in a beautiful
(and IMHO underappreciated) paper in the

Atkin-Lehner
symmetry"), where it was demonstrated in an example that the tachyon
can make the dominant contribution in a heterotic string loop, despite
the fact that the tachyon is GSO-projected out and thus cannot appear
as external particle.

[The aim of that paper was to see whether one can get vanishing
loop amplitudes (such as the vacuum energy) in non-supersymmetric
theories, as an effect of these "extra" contributions to loop
amplitudes; the idea was that in order for an amplitude to vanish,
it it not necessary that the integrand dumbly vanishes term by term (as
in a susy theory), but all what is necessary is that the modular
integral over it vanishes (which is obviously a weaker condition).]

In a nutshell, already perturbative string theory is much more than
particle quantum field theory (not to speak about non-pertubative
properties).
In view of this, one may ponder whether it is a good idea to
use particle QFT intuition for addressing questions like the
vanishing of the vacuum energy or scalar self-energies, etc; but that's
another topic.

As far as the main question of the thread is concerned:
Lubos answered it at length, let me summarize it in two sentences:

String theory does not predict GR (in the sense of Einstein's
lagrangian) in the low energy effective action, but GR with infinitely
many corrections (eg higher powers in the curvature, which however
play no role at macroscopic scales). What string theory guarantees
is general coordinate invariance of this effective action, and this
as a consequence of the conformal symmetry of the world-sheet theory.

-WL

Aug22-04, 02:42 PM

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','to olbar=no,location=no,scrollbars=yes,resizable=yes, status=no,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usene t 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, 21 Aug 2004, Wolfgang Lerche wrote:\n\n> It is a subtle but important point that string theory\n> amplitudes should not be interpreted/viewed as simple superposition\n> of particle amplitudes with a cutoff. At one loop, one can see this\n> by noting that the lower boundary of the fundamental domain is\n> curved and not a straight line. If it were straight, it would\n> amount to a projection on excitations that obey N_L=N_R (this\n> projection is in force on external legs which can be thought of as\n> thin cylinders; that is, external particles must satisfy that\n> well-known condition, actually it is one of the conditions for\n> physical states).\n\nGood point. I agree that this subtlety is important for string theory\'s\nability to avoid various inconsistencies.\n\nThe question whether the states violating N_L=N_R propagate in the loop or\nnot used to be a very interesting one - at least for me when I was a\nstudent. If I remember well, the final answer I decided to believe - after\ndiscussions with my advisor Tom Banks - was not quite the same answer that\nyou proposed. Well, it seems obvious that the fundamental domain is *not*\na Cartesian product of the interval (-1/2, +1/2) times something else, and\nin this sense it also counts N_L=N_R violating states.\n\nOn the other hand, you can still formally think of the integral over the\nfundamental domain to be the integral over the whole upper half plane,\ndivided by the (infinite) number of the copies of the fundamental domain\nfound in the upper half plane. The integral over the upper half-plane is\ninvariant under the translation of tau by a real number, and therefore it\n*does* guarantee that only the states with N_L=N_R contribute.\n\nThe previous argument is formal because the final result was obtained as\nthe "infinity/infinity" ratio. However, this problem can disappear if you\nconsider a compactification on a torus, for example. The torus stringy\npath integral, in this case, also includes the summation over the pair of\nwinding numbers (around the two periods of the worldsheet torus), and the\nintegral over the fundamental domain. These integrals can be rewritten as\nthe integral over the whole upper half plane, and the summation is already\nincluded - or at least reduced from the summation over arbitrary pairs of\nintegers to a much smaller set. Am I wrong? My slow modem does not allow\nme to check this statement too carefully. ;-)\n\nIf the argument is correct, the one-loop stringy amplitudes for a\ntorus-compactified background *can* be written as a summation over states\nthat satisfy N_L=N_R (plus n.w, momentum times winding). Perhaps there is\nsome subtlety that makes the argument sick when the winding(s) vanish. We\nshould try to resolve this problem in detail. ;-)\n\n> This means that the intricate properties of string loops, and\n> specifically those which make they theory consistent, cannot be\n> captured by summing naive particle QFT (well, that\'s not a theorem\n> but I think it is quite obvious).\n\nI agree that the ways how to make a UV theory with all these consistency\nrequirements are severely restricted, and probably reduce to possible and\nknown string theories (perhaps plus some theories that have infinitely\nmany parameters and are unpredictive). But one can still write string\ntheory as string field theory, cannot she? Then we obtain a QFT-like\ndescription of a theory without UV problems, and the moduli spaces are\ndivided into regions corresponding to particular QFT diagrams. Is it true?\n\n> This had first been put into this context by Greg Moore in a beautiful\n> (and IMHO underappreciated) paper in the mid-80\'s ("Atkin-Lehner\n> symmetry"), where it was demonstrated in an example that the tachyon\n> can make the dominant contribution in a heterotic string loop, despite\n> the fact that the tachyon is GSO-projected out and thus cannot appear\n> as external particle.\n\nInteresting.\n\n> In a nutshell, already perturbative string theory is much more than\n> particle quantum field theory (not to speak about non-pertubative\n> properties).\n\nRight & agreements with the rest.\n\nBest regards\nLubos\n__________________________________ ____________________________________________\nE-mail: lumo@matfyz.cz fax: +1-617/496-0110 Web: http://lumo.matfyz.cz/\neFax: +1-801/454-1858 work: +1-617/496-8199 home: +1-617/868-4487 (call)\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, 21 Aug 2004, Wolfgang Lerche wrote:

> It is a subtle but important point that string theory
> amplitudes should not be interpreted/viewed as simple superposition
> of particle amplitudes with a cutoff. At one loop, one can see this
> by noting that the lower boundary of the fundamental domain is
> curved and not a straight line. If it were straight, it would
> amount to a projection on excitations that obey

(this
> projection is in force on external legs which can be thought of as
> thin cylinders; that is, external particles must satisfy that
> well-known condition, actually it is one of the conditions for
> physical states).

Good point. I agree that this subtlety is important for string theory's
ability to avoid various inconsistencies.

The question whether the states violating

propagate in the loop or
not used to be a very interesting one

least for me when I was a
student. If I remember well, the final answer I decided to believe - after
discussions with my advisor Tom Banks - was not quite the same answer that
you proposed. Well, it seems obvious that the fundamental domain is *not*
a Cartesian product of the interval

times something else, and
in this sense it also counts

violating states.

On the other hand, you can still formally think of the integral over the
fundamental domain to be the integral over the whole upper half plane,
divided by the (infinite) number of the copies of the fundamental domain
found in the upper half plane. The integral over the upper half-plane is
invariant under the translation of $LaTeX Code: \\tau$ by a real number, and therefore it
*does* guarantee that only the states with

contribute.

The previous argument is formal because the final result was obtained as
the "infinity/infinity" ratio. However, this problem can disappear if you
consider a compactification on a torus, for example. The torus stringy
path integral, in this case, also includes the summation over the pair of
winding numbers (around the two periods of the worldsheet torus), and the
integral over the fundamental domain. These integrals can be rewritten as
the integral over the whole upper half plane, and the summation is already
included - or at least reduced from the summation over arbitrary pairs of
integers to a much smaller set. Am I wrong? My slow modem does not allow
me to check this statement too carefully. ;-)

If the argument is correct, the one-loop stringy amplitudes for a
torus-compactified background *can* be written as a summation over states
that satisfy

(plus n.w, momentum times winding). Perhaps there is
some subtlety that makes the argument sick when the winding(s) vanish. We
should try to resolve this problem in detail. ;-)

> This means that the intricate properties of string loops, and
> specifically those which make they theory consistent, cannot be
> captured by summing naive particle QFT (well, that's not a theorem
> but I think it is quite obvious).

I agree that the ways how to make a UV theory with all these consistency
requirements are severely restricted, and probably reduce to possible and
known string theories (perhaps plus some theories that have infinitely
many parameters and are unpredictive). But one can still write string
theory as string field theory, cannot she? Then we obtain a QFT-like
description of a theory without UV problems, and the moduli spaces are
divided into regions corresponding to particular QFT diagrams. Is it true?

> This had first been put into this context by Greg Moore in a beautiful
> (and IMHO underappreciated) paper in the

Atkin-Lehner
> symmetry"), where it was demonstrated in an example that the tachyon
> can make the dominant contribution in a heterotic string loop, despite
> the fact that the tachyon is GSO-projected out and thus cannot appear
> as external particle.

Interesting.

> In a nutshell, already perturbative string theory is much more than
> particle quantum field theory (not to speak about non-pertubative
> properties).

Right & agreements with the rest.

Best regards
Lubos
__{_______________________________________________ _____________________________}
E-mail: lumo@matfyz.cz fax:

Web: http://lumo.matfyz.cz/
eFax:

work:

home:

(call)
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^

Aug23-04, 04:06 AM

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','to olbar=no,location=no,scrollbars=yes,resizable=yes, status=no,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usene t 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 Motl <motl@feynman.harvard.edu> wrote in message news:<Pine.LNX.4.31.0408221425450.29544-100000@feynman.harvard.edu>...\n> On Sat, 21 Aug 2004, Wolfgang Lerche wrote:\n>\n>\n> The question whether the states violating N_L=N_R propagate in the loop or\n> not used to be a very interesting one - at least for me when I was a\n> student. If I remember well, the final answer I decided to believe - after\n> discussions with my advisor Tom Banks - was not quite the same answer that\n> you proposed. Well, it seems obvious that the fundamental domain is *not*\n> a Cartesian product of the interval (-1/2, +1/2) times something else, and\n> in this sense it also counts N_L=N_R violating states.\n\nBTW, I meant to write M_L=M_R, but that should have been obvious from\nthe context...\n\n> On the other hand, you can still formally think of the integral over the\n> fundamental domain to be the integral over the whole upper half plane,\n> divided by the (infinite) number of the copies of the fundamental domain\n> found in the upper half plane. The integral over the upper half-plane is\n> invariant under the translation of tau by a real number, and therefore it\n> *does* guarantee that only the states with N_L=N_R contribute.\n\nThis argument would work immediately if one would tesselate the\nupper half-plane by rectangles (which could be generated by an\nobvious group action), but this would not describe what the path\nintegral instructs us to do, namely summing over precisely one copy\nof the torus (and is what makes it distinct as compared to a particle\nQFT loop). For a tesselation via curved fundamental domains, your\nargument may fail due to infinity/infinity, as you pointed out; to\nsee what precisely happens would require a careful regularizatiuon.\n\n\n> But one can still write string\n> theory as string field theory, cannot she? Then we obtain a QFT-like\n> description of a theory without UV problems, and the moduli spaces are\n> divided into regions corresponding to particular QFT diagrams. Is it true?\n\nI think there is extra information in the game that goes beyond\nparticle QFT, namely from the interior regions of the moduli space.\nThe SFT diagrams are "fat" and the particle diagrams are "thin" and\ncorrespond to a degenerating limit of the former (topologically the\ndiagrams are the same). Only in this limit there is agreemennt;\nin other words, the moment you pinch a riemann surface (so as to\ndevelop an infinitely thin tube), the M_L=M_R projection is in\neffect, which means that singularities arise due to\nphysical states only. But for the interior of the moduli space,\nwhich rougly corresponds to "fattened" diagrams, there are extra\nstringy contributions that have no analog in particle theory - at\nleast this is how I think about it.\n\nFor example, the log (IR) divergence in the 1-loop gauge coupling\ncomes from Im(tau)->infty where the torus becomes a thin tube, and\nso only physical states with M_L=M_R contribute to it. On the other\nhand,\nfor the bulk 1-loop vacuum amplidute:\n\n> >..., where it was demonstrated in an example that the tachyon\n> > can make the dominant contribution in a heterotic string loop, despite\n> > the fact that the tachyon is GSO-projected out and thus cannot appear\n> > as external particle.\n>\nThis is an explicit example for a state which violates M_L = M_R but\ndoes\ncontribute in the loop - see more details on p 31/32 in:\nhttp://ccdb3fs.kek.jp/cgi-bin/img/allpdf?198705249\nHowever, one needs to be careful as the shape of the fundamental\nregion is not an invariant statement, and in a transformed region\nthe interpretation of what state contributes how much may be\ndifferent.\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>Lubos Motl <motl@feynman.harvard.edu> wrote in message news:<Pine.LNX.4.31.0408221425450.29...arvard.edu>...
> On Sat, 21 Aug 2004, Wolfgang Lerche wrote:
>
>
> The question whether the states violating

propagate in the loop or
> not used to be a very interesting one

least for me when I was a
> student. If I remember well, the final answer I decided to believe - after
> discussions with my advisor Tom Banks - was not quite the same answer that
> you proposed. Well, it seems obvious that the fundamental domain is *not*
> a Cartesian product of the interval

times something else, and
> in this sense it also counts

violating states.

BTW, I meant to write

but that should have been obvious from
the context...

> On the other hand, you can still formally think of the integral over the
> fundamental domain to be the integral over the whole upper half plane,
> divided by the (infinite) number of the copies of the fundamental domain
> found in the upper half plane. The integral over the upper half-plane is
> invariant under the translation of $LaTeX Code: \\tau$ by a real number, and therefore it
> *does* guarantee that only the states with

contribute.

This argument would work immediately if one would tesselate the
upper half-plane by rectangles (which could be generated by an
obvious group action), but this would not describe what the path
integral instructs us to do, namely summing over precisely one copy
of the torus (and is what makes it distinct as compared to a particle
QFT loop). For a tesselation via curved fundamental domains, your
argument may fail due to infinity/infinity, as you pointed out; to
see what precisely happens would require a careful regularizatiuon.

> But one can still write string
> theory as string field theory, cannot she? Then we obtain a QFT-like
> description of a theory without UV problems, and the moduli spaces are
> divided into regions corresponding to particular QFT diagrams. Is it true?

I think there is extra information in the game that goes beyond
particle QFT, namely from the interior regions of the moduli space.
The SFT diagrams are "fat" and the particle diagrams are "thin" and
correspond to a degenerating limit of the former (topologically the
diagrams are the same). Only in this limit there is agreemennt;
in other words, the moment you pinch a riemann surface (so as to
develop an infinitely thin tube), the

projection is in
effect, which means that singularities arise due to
physical states only. But for the interior of the moduli space,
which rougly corresponds to "fattened" diagrams, there are extra
stringy contributions that have no analog in particle theory

least this is how I think about it.

For example, the log (IR) divergence in the 1-loop gauge coupling
comes from $LaTeX Code: Im(\\tau)->\\infty$ where the torus becomes a thin tube, and
so only physical states with

contribute to it. On the other
hand,
for the bulk 1-loop vacuum amplidute:

> >..., where it was demonstrated in an example that the tachyon
> > can make the dominant contribution in a heterotic string loop, despite
> > the fact that the tachyon is GSO-projected out and thus cannot appear
> > as external particle.
>
This is an explicit example for a state which violates

but
does
contribute in the loop - see more details on

in:
http://ccdb3fs.kek.jp/cgi-bin/img/allpdf?198705249
However, one needs to be careful as the shape of the fundamental
region is not an invariant statement, and in a transformed region
the interpretation of what state contributes how much may be
different.

-W

Aug23-04, 09:35 AM

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','to olbar=no,location=no,scrollbars=yes,resizable=yes, status=no,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usene t 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>"WL" <wolfgang.lerche@cern.ch> schrieb im Newsbeitrag\nnews:78c7d685.0408230005.8c24ce5-100000@posting.google.com...\n> Lubos Motl <motl@feynman.harvard.edu> wrote in message\nnews:<Pine.LNX.4.31.0408221425450.2954 4-100000@feynman.harvard.edu>...\n\n> > But one can still write string\n> > theory as string field theory, cannot she? Then we obtain a QFT-like\n> > description of a theory without UV problems, and the moduli spaces are\n> > divided into regions corresponding to particular QFT diagrams. Is it\ntrue?\n>\n> I think there is extra information in the game that goes beyond\n> particle QFT, namely from the interior regions of the moduli space.\n\nWhen the action of string field theory is expanded in component fields and\nthe CFT/Hilbert space parts are evaluated (e.g. when the cubic vertex is\nevaluated) then one is left with an "ordinary" field theory in terms of\nthese component fields, albeit a non-local one with infinitely many\ndifferent fields all interacting with each other. Isn\'t it?\n\n(Of course most of these fields are "off-shell" in the sense that they\ncorrespond to string states which are not BRST closed.)\n\nI don\'t think this is in contradiction to what has been said here before,\nbut it should mean that there is at least one point of view from which all\nstring scattering can be regarded as pure point particle field theory. But\nwhen saying this it is certainly crucial that this particle field theory is\nnon-local and contains infinitely many fields, properties which are shadows\nof the string degrees of freedom that have been "integrated out".\n\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>"WL" <wolfgang.lerche@cern.ch> schrieb im Newsbeitrag
news:78c7d685.0408230005.8c24ce5-100....google.com...
> Lubos Motl <motl@feynman.harvard.edu> wrote in message
news:<Pine.LNX.4.31.0408221425450.29...arvard.edu>...

> > But one can still write string
> > theory as string field theory, cannot she? Then we obtain a QFT-like
> > description of a theory without UV problems, and the moduli spaces are
> > divided into regions corresponding to particular QFT diagrams. Is it
true?
>
> I think there is extra information in the game that goes beyond
> particle QFT, namely from the interior regions of the moduli space.

When the action of string field theory is expanded in component fields and
the CFT/Hilbert space parts are evaluated (e.g. when the cubic vertex is
evaluated) then one is left with an "ordinary" field theory in terms of
these component fields, albeit a non-local one with infinitely many
different fields all interacting with each other. Isn't it?

(Of course most of these fields are "off-shell" in the sense that they
correspond to string states which are not BRST closed.)

I don't think this is in contradiction to what has been said here before,
but it should mean that there is at least one point of view from which all
string scattering can be regarded as pure point particle field theory. But
when saying this it is certainly crucial that this particle field theory is
non-local and contains infinitely many fields, properties which are shadows
of the string degrees of freedom that have been "integrated out".

Aug24-04, 12:45 AM

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','to olbar=no,location=no,scrollbars=yes,resizable=yes, status=no,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usene t 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 all,\n\nI am confused about two technical statements made in this\nconversation:\n\n1. In "plumbing constrcutions" that try to obtain string scattering\namplitudes from string Feynman diagrams, i.e divide the Riemann\nsurface to vertices and propagators (the latter have all off-shell\nstring modes propagating), the propagators are always topologically a\ncylinder, and the integration over\nthe compact modulus then enforces level matching for the propagating\nmodes (which are still off-shell). Relatedly (I think), in closed\nstring field theory, one does impose level matching for off-shell\nfields.\n\nThe one-loop, zero temperature, partition fucntion seem to have some\nextra magic,\nI wonder how is that reproduced in SFT...\n\n2. I am confused about the statement that the tachyon contributes to\none loop heterotic amplitudes. The tachyon is projected out by GSO,\nwhich is an exact worldsheet gauge symmetry, imposed off-shell as\nwell, I thought. Maybe I should read the paper...\n\nbest,\nMoshe\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 all,

I am confused about two technical statements made in this
conversation:

1. In "plumbing constrcutions" that try to obtain string scattering
amplitudes from string Feynman diagrams, i.e divide the Riemann
surface to vertices and propagators (the latter have all off-shell
string modes propagating), the propagators are always topologically a
cylinder, and the integration over
the compact modulus then enforces level matching for the propagating
modes (which are still off-shell). Relatedly (I think), in closed
string field theory, one does impose level matching for off-shell
fields.

The one-loop, zero temperature, partition fucntion seem to have some
extra magic,
I wonder how is that reproduced in SFT...

2. I am confused about the statement that the tachyon contributes to
one loop heterotic amplitudes. The tachyon is projected out by GSO,
which is an exact worldsheet gauge symmetry, imposed off-shell as
well, I thought. Maybe I should read the paper...

best,
Moshe

Aug24-04, 08:40 AM

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','to olbar=no,location=no,scrollbars=yes,resizable=yes, status=no,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usene t 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>Moshe Rozali <rozali@physics.ubc.ca> wrote in message news:<4a66eedc.0408231223.56ef44f7-100000@posting.google.com>...\n\nHi,\n\n> The one-loop, zero temperature, partition fucntion seem to have some\n> extra magic,\n> I wonder how is that reproduced in SFT...\n\nSFT experts should know the answer; I remember it has been an issue\nin the past to see how the plumbing of pants and tubes reproduces\nthe moduli space of riemann surfaces. And this is simply not the\ndirect product of "Schwinger parameters" and angular coordinates\naround cylinders (it is this direct product structure what I had\nin mind when referring to "particle QFT").\n>\n> 2. I am confused about the statement that the tachyon contributes to\n> one loop heterotic amplitudes. The tachyon is projected out by GSO,\n> which is an exact worldsheet gauge symmetry, imposed off-shell as\n> well, I thought. Maybe I should read the paper...\n\nActually I didn\'t recall it correctly- in the non-supersymmetric\nexample construction, the tachyon is _not_ GSO-projected out,\nbut violates the M_L=M_R condition, so is not a physical state. It\ncontributes to the 1-loop amplitude which then at the end vanishes,\ndespite the theory not being supersymmetric.\n\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>Moshe Rozali <rozali@physics.ubc.ca> wrote in message news:<4a66eedc.0408231223.56ef44f7-1...google.com>...

Hi,

> The one-loop, zero temperature, partition fucntion seem to have some
> extra magic,
> I wonder how is that reproduced in SFT...

SFT experts should know the answer; I remember it has been an issue
in the past to see how the plumbing of pants and tubes reproduces
the moduli space of riemann surfaces. And this is simply not the
direct product of "Schwinger parameters" and angular coordinates
around cylinders (it is this direct product structure what I had
in mind when referring to "particle QFT").
>
> 2. I am confused about the statement that the tachyon contributes to
> one loop heterotic amplitudes. The tachyon is projected out by GSO,
> which is an exact worldsheet gauge symmetry, imposed off-shell as
> well, I thought. Maybe I should read the paper...

Actually I didn't recall it correctly- in the non-supersymmetric
example construction, the tachyon is _not_ GSO-projected out,
but violates the

condition, so is not a physical state. It
contributes to the 1-loop amplitude which then at the end vanishes,
despite the theory not being supersymmetric.

-W

Aug24-04, 08:40 AM

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','to olbar=no,location=no,scrollbars=yes,resizable=yes, status=no,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usene t 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>> GR and the calculations are done differently in these two theories. The\n> question "what is the local symmetry group of Nature" is not really\n> well-defined - the local symmetry group depends on the degrees of freedom\n> that we start with; the role of the local symmetry group is to remove some\n> degrees of freedom. The gauge group describes *redundancy* of our\n> description. In general, there exist different equivalent starting points\n> with different gauge symmetries that nevertheless reproduce the same\n> physics - because of Seiberg dualities and S-dualities, holography, matrix\n> models, higgsing, unhiggshing, and confinement, and other equivalences.\n\nI am not sure. does the gauge group really describe the redundancy of\nthe theory? well the redundancies of e.g. U(1) are removed if you use\nfields F=dA instead of potentials A. (although this formulation\ncertainly would be nonlocal, topological - AharonovBohm-effect).\ndoesn\'t the original symmetry one started with remain somehow (or\nrestrict) the lagrangian describing the interaction of the fields F?\nso that the symmetry still appear in a disguised form?\nCan the symmetries of gravity (diff. invariance) also be removed in\nsuch a way?\n\n-EG\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>> GR and the calculations are done differently in these two theories. The
> question "what is the local symmetry group of Nature" is not really
> well-defined - the local symmetry group depends on the degrees of freedom
> that we start with; the role of the local symmetry group is to remove some
> degrees of freedom. The gauge group describes *redundancy* of our
> description. In general, there exist different equivalent starting points
> with different gauge symmetries that nevertheless reproduce the same
> physics - because of Seiberg dualities and S-dualities, holography, matrix
> models, higgsing, unhiggshing, and confinement, and other equivalences.

I am not sure. does the gauge group really describe the redundancy of
the theory? well the redundancies of e.g. U(1) are removed if you use
fields

instead of potentials A. (although this formulation
certainly would be nonlocal, topological - AharonovBohm-effect).
doesn't the original symmetry one started with remain somehow (or
restrict) the lagrangian describing the interaction of the fields F?
so that the symmetry still appear in a disguised form?
Can the symmetries of gravity (diff. invariance) also be removed in
such a way?

-EG

Aug24-04, 01:45 PM

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','to olbar=no,location=no,scrollbars=yes,resizable=yes, status=no,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usene t 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>"josef hader" <gary.larson@gmx.at> schrieb im Newsbeitrag\nnews:98f5d48d.0408240357.693430d7-100000@posting.google.com...\n\n> I am not sure. does the gauge group really describe the redundancy of\n> the theory?\n\nYes. That\'s why it is called "gauge".\n\nYou can fix a certain gauge, meaning that you pick by hand one\nrepresentative of the gauge group "in every fiber". In electromagnetism such\ngauges are known as "Coulomb gauge", "Lorentz gauge", etc. In GR such gauges\n(choices of coordinates) are known as "Riemann normal coordinates",\n"Eddington-Finkelstein" coordinates, etc.\n\n> well the redundancies of e.g. U(1) are removed if you use\n> fields F=dA instead of potentials A.\n\nNo, that\'s not the idea. Writing F = dA does not remove the gauge freedom\nbut merely provides you with a _gauge invariant observable_, meaning that\nthe value of F is independent of the gauge choice you made.\n\n> (although this formulation\n> certainly would be nonlocal, topological - AharonovBohm-effect).\n\nNo, writing F=dA does not involve a "formulation" of the theory. F is a\ngauge invariant quantitiy. Nothing more, nothing less.\n\n> doesn\'t the original symmetry one started with remain somehow (or\n> restrict) the lagrangian describing the interaction of the fields F?\n\nYou can use the Lagrangian in its not-gauge-fixed form. In ptah integral\nquantization this leads to a summation about all gauge equivalent field\nconfigurations (which are physically all the same) leading to usually\ndiverging contributions which have to be devided out.\n\nOne very elegant way to do this is to fix a gauge by inserting an\nappropriate delta-distribution into the path integral (restricting\nintegration to a certain "gauge slice"). Due to the rules of\ndelta-distributions this has to be accompanied by a certain derterminant\nthat ensures the correct measure in the integral. This determinant can\nconveniently be expressed as an integral over anticommuting Grassmann\nintegrals. The delta-distribution itself can be expressed in its Fourier\nform, so that all in all we can rewrite the resulting gauge fixed path\nintegral by substituting the integrand\n\nexp(iS)\n\nfor the plain action S of the system by\n\nexp(i (S + S_f + S_g ) )\n\nwhere S_f is the part describing the gaugeFixing delta distribution and S_g\nis the Grassmann term.\n\nThe resulting total action\n\nS + S_f + S_g\n\nis the BRST action of the system and quantizing this is the by far most\nelegant and sophisticated way to handle systems with gauge symmetries that\nmankind has thought up so far.\n\nThat\'s because this action effectively fixes the gauge and hence removes all\nthe gauge freedom, but it really does so by adding new fields, the Grassmann\nvariables (called "ghosts"). The point is that the dynamics of these\nauxiliary degrees of freedom takes care of all aspects of gauge fixing,\nwhile the dynamics of the whole system is formally that of an unconmstrained\nsystem.\n\n> Can the symmetries of gravity (diff. invariance) also be removed in\n> such a way?\n\nYes, indeed. The most well-studied example is the gauge fixing of 1+1\ndimensional (super)gravity, which leads to the BRST quantization of the\nstring.\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>"josef hader" <gary.larson@gmx.at> schrieb im Newsbeitrag
news:98f5d48d.0408240357.693430d7-10....google.com...

> I am not sure. does the gauge group really describe the redundancy of
> the theory?

Yes. That's why it is called "gauge".

You can fix a certain gauge, meaning that you pick by hand one
representative of the gauge group "in every fiber". In electromagnetism such
gauges are known as "Coulomb gauge", "Lorentz gauge", etc. In GR such gauges
(choices of coordinates) are known as "Riemann normal coordinates",
"Eddington-Finkelstein" coordinates, etc.

> well the redundancies of e.g. U(1) are removed if you use
> fields

instead of potentials A.

No, that's not the idea. Writing

does not remove the gauge freedom
but merely provides you with a _gauge invariant

meaning that
the value of F is independent of the gauge choice you made.

> (although this formulation
> certainly would be nonlocal, topological - AharonovBohm-effect).

No, writing

does not involve a "formulation" of the theory. F is a
gauge invariant quantitiy. Nothing more, nothing less.

> doesn't the original symmetry one started with remain somehow (or
> restrict) the lagrangian describing the interaction of the fields F?

You can use the Lagrangian in its not-gauge-fixed form. In ptah integral
quantization this leads to a summation about all gauge equivalent field
configurations (which are physically all the same) leading to usually
diverging contributions which have to be devided out.

One very elegant way to do this is to fix a gauge by inserting an
appropriate $LaTeX Code: \\delta-distribution$ into the path integral (restricting
integration to a certain "gauge slice"). Due to the rules of
$LaTeX Code: \\delta-distributions$ this has to be accompanied by a certain derterminant
that ensures the correct measure in the integral. This determinant can
conveniently be expressed as an integral over anticommuting Grassmann
integrals. The $LaTeX Code: \\delta-distribution$ itself can be expressed in its Fourier
form, so that all in all we can rewrite the resulting gauge fixed path
integral by substituting the integrand

$LaTeX Code: \\exp(iS)$

for the plain action S of the system by

$LaTeX Code: \\exp(i (S + S_f + S_g ) )$

where

is the part describing the gaugeFixing $LaTeX Code: \\delta$ distribution and

is the Grassmann term.

The resulting total action

is the BRST action of the system and quantizing this is the by far most
elegant and sophisticated way to handle systems with gauge symmetries that
mankind has thought up so far.

That's because this action effectively fixes the gauge and hence removes all
the gauge freedom, but it really does so by adding new fields, the Grassmann
variables (called "ghosts"). The point is that the dynamics of these
auxiliary degrees of freedom takes care of all aspects of gauge fixing,
while the dynamics of the whole system is formally that of an unconmstrained
system.

> Can the symmetries of gravity (diff. invariance) also be removed in
> such a way?

Yes, indeed. The most well-studied example is the gauge fixing of 1+1
dimensional (super)gravity, which leads to the BRST quantization of the
string.

**Haelfix** · Sep3-04, 05:32 AM

Ok, this answers the question I posed several months ago here, but never got a reply.

If there are corrections to field theoretic GR (or well SUGRA) at say 2 loops, why exactly aren't we testing for such phenomena. Is it simply that the probes are too weak, eg that the coupling constant alpha is too small... Still, wouldn't something like LIGO be applicable, or at least something in *principle*.

I'm pretty sure they already are trying to test for quantum corrections in 1 loop gravity on some soon to depart satellite.. If the nonrenormalizable field theoretic description and the stringy description start departing at 2 loops, I don't see why that isn't testable a priori.

I mean, how many orders of magnitude is experiment off in the ideal situation? Surely something can be contrived such that it wouldn't be tiny perturbations the likes of a Planck scale. Say perhaps around a strong gravitational source like a Neutron star, where the classical theory is pretty well understood.

Sep7-04, 08:10 AM

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','to olbar=no,location=no,scrollbars=yes,resizable=yes, status=no,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usene t 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>Haelfix <haelfix@hotmail.com> wrote in\n\n> (...) If there are corrections to field theoretic GR (or well SUGRA) at say 2\n> loops, why exactly aren\'t we testing for such phenomena. Is it simply\n> that the probes are too weak, eg that the coupling constant alpha is\n> too small...\n\nYou mean alpha\' the (inverse) string tension. Yes, it is much too\nsmall. We would need to create curvature on the order of the Planck\nscale.\n\n> Still, wouldn\'t something like LIGO be applicable, or at\n> least something in *principle*.\n\nIf "in principle" means given a source of gravitational waves with\namplitude 1 (rather than much much much smaller), then yes.\n\n\n> I\'m pretty sure they already are trying to test for quantum corrections\n> in 1 loop gravity on some soon to depart satellite.\n\nI don\'t think so. I suppose this is STEP, which is the equivalence\nprinciple, or in other words tests for light force-carrier fields\nbeyond the photon and graviton. This is not alpha\' corrections.\n\n> If the\n> nonrenormalizable field theoretic description and the stringy\n> description start departing at 2 loops, I don\'t see why that isn\'t\n> testable a priori.\n\nBut not in practice.\n\n> I mean, how many orders of magnitude is experiment off in the ideal\n> situation? Surely something can be contrived such that it wouldn\'t be\n> tiny perturbations the likes of a Planck scale. Say perhaps around a\n> strong gravitational source like a Neutron star, where the classical\n> theory is pretty well understood.\n\nI don\'t feel like doing the numerical estimates now, but rest assured,\nthe curvature around a neutron star is *nowhere* near the Planck\nscale!\n\nThomas\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>Haelfix <haelfix@hotmail.com> wrote in

> (...) If there are corrections to field theoretic GR (or well SUGRA) at say 2
> loops, why exactly aren't we testing for such phenomena. Is it simply
> that the probes are too weak, eg that the coupling constant $LaTeX Code: \\alpha$ is
> too small...

You mean $LaTeX Code: \\alphasingle-quote$ the (inverse) string tension. Yes, it is much too
small. We would need to create curvature on the order of the Planck
scale.

> Still, wouldn't something like LIGO be applicable, or at
> least something in *principle*.

If "in principle" means given a source of gravitational waves with
amplitude 1 (rather than much much much smaller), then yes.

> I'm pretty sure they already are trying to test for quantum corrections
> in 1 loop gravity on some soon to depart satellite.

I don't think so. I suppose this is STEP, which is the equivalence
principle, or in other words tests for light force-carrier fields
beyond the photon and graviton. This is not $LaTeX Code: \\alphasingle-quote$ corrections.

> If the
> nonrenormalizable field theoretic description and the stringy
> description start departing at 2 loops, I don't see why that isn't
> testable a priori.

But not in practice.

> I mean, how many orders of magnitude is experiment off in the ideal
> situation? Surely something can be contrived such that it wouldn't be
> tiny perturbations the likes of a Planck scale. Say perhaps around a
> strong gravitational source like a Neutron star, where the classical
> theory is pretty well understood.

I don't feel like doing the numerical estimates now, but rest assured,
the curvature around a neutron star is *nowhere* near the Planck
scale!

Thomas