View Full Version : Paper of the day - twistors & conf. gravity
Lubos Motl
Jun6-04, 10:35 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>Well, today I vote for Berkovits and Witten\n\nhttp://www.arxiv.org/abs/hep-th/0406051\n\nAfter my initial fast reading, it\'s clear that it\'s a very smoothly\nreadable - and eagerly expected by many - analysis of the gravity-like\nstates found in both major twistorial pictures for N=4 super Yang-Mills,\npictures due to Witten and Berkovits, respectively. The reader is supposed\nto be familiar with the basic statements of this twistor-Yang-Mills story,\notherwise the text below will be useless for her. The following PowerPoint\nXP (more precisely, PowerString PX+i\\hbar) file may be useful:\n\nhttp://schwinger.harvard.edu/~motl/twistors.ppt\n\nFirst of all, unlike many others, Berkovits and Witten treat these\nconformal gravity states as a problem - something that potentially hurts\nthe exact relation with the N=4 super Yang-Mills S-matrix, and they\npresent some evidence - one might perhaps say a proof - that the loop\ndiagrams are damaged by the intermediate gravity states indeed, at the end\nof their article, and therefore the twistorial string theories disagree\nwith Yang-Mills theory at the loop level.\n\n(I fully sympathize with this "critical" approach. As you know, I don\'t\nbelieve that one can construct a meaningful quantum theory of gravity\nstarting from the conformal gravity and making a few small steps - this\nwould indeed be a counterexample to the principle that string theory is\nthe only theory of quantum gravity. These theories are not theories\ncontaining meaningful gravity, because of the presence of ghosts, and they\nalso don\'t seem to be exactly Yang-Mills because the spectrum has these\nconformal gravity exotics.)\n\nNevertheless they compute many details about the gauge-singlets appearing\nin these twistor pictures. The effective action described by these new\nsinglet states, a topic that they study in depth, has inevitably the\nsuperconformal symmetry, inherited from the geometry of the supertwistor\nspace. This implies that the highest-helicity bosonic part\'s kinetic terms\nmust be of the form (Weyl tensor squared). Although it is a problematic\naction due to the appearance of ghosts (negative-norm states, much like in\na scalar "phi box squared phi" theories which is equivalent to TWO scalar\nfields with the OPPOSITE signs of the kinetic terms), many steps, such as\nthe separation to the self-dual and the anti-self-dual piece, follow in\nanalogy with the gauge theory case. Just the number of indices is doubled\n- four spinor indices, describing helicities between -2 and +2.\n\nThe extra gravity states look like volume-preserving vector fields on the\ntwistor space, or something along these lines, and an extra B-field\nprovides us with the opposite helicity states. Various details are studied\nin the spacetime picture, Berkovits\' model, Witten\'s model, or some\ncombination of the three.\n\nThe Minkowski spacetime translation generator is found to be\nnon-diagonalizable (Jordan blocks generalizing the nilpotent matrices)\nwhich is an example how these theories break unitarity. The spectrum of\nthe (multiplet of the) theory has excitations with helicities between -2\nand +2; their precise composition looks unusual.\n\nBerkovits and Witten compute the three-point functions and MHV tree\namplitudes, and compare them with Witten\'s B-model. These are somewhat\nless familiar than the gauge theory case, but they may be interesting.\n\nI was happy to see various technical details to be written in a way that I\nagree with - for example Nathan now agreed that on the Euclidean\nworldsheet of his string, the twistors are complex, and they\'re only\nconstrained to be real on the worldsheet\'s boundary - much like in\nNeitzke-Vafa, in a sense.\n\nIn the final section 7 they study potential restrictions on the gauge\ngroup. Although I have not absorbed all the details, there is some\npossibility to derive the Berkovits\' constraint c=28 in the B-model, too,\nalthough the gauge groups on both sides are different. Witten\'s B-model\nwould seem to allow U(28), for example, while products of U(1) and SU(2)\ncurrent algebras at various levels are discussed on Berkovits\' side. It\nseems to me that Berkovits\' and Witten\'s pictures are not quite equivalent\neither, and the overall story (at least so far) certainly looks less\nbeautiful than the derivation of the two possible type I gauge groups in\nten dimensions (namely SO(32) and E_8\\times E_8).\n\nIf I tried to make some conclusions, I would say that the present paper\nmight invalidate the exact map between the twistorial string theories and\nthe Yang-Mills S-matrix at the quantum (loop) level, which may imply that\nthe agreement at the tree level is something that may be guaranteed by\nsymmetries. This would mean that the twistorial string theories, and their\ndetailed technical features and differences in particular, are not\nterribly fundamental - assuming that the N=4 gauge theory as we know it\n*is* fundamental. Nevertheless the tree-level S-matrix of exotic theories\nsuch as the conformal supergravity seems to have a comparably efficient\ndescription in terms of the supertwistor space, which may be interesting\nat least for those who think that conformal supergravity theories are\nimportant.\n\nSo far, I can still imagine that the twistorial framework offers new,\nvery different and very efficient tools to calculate the loop amplitudes -\nusing very different integrals than those over the loop momenta - but it\nnow seems unlikely that these loop amplitudes are what one would derive in\nthe most straightforward and controllable ways from the twistor-string\ntheories that have been presented.\n\nDifferent points of view are more than welcome.\n\nAll the best\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\n[Posted for the 2nd time because of continuing problems with the FAS\nnewsserver. LM]\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>Well, today I vote for Berkovits and Witten
http://www.arxiv.org/abs/http://www.arxiv.org/abs/hep-th/0406051
After my initial fast reading, it's clear that it's a very smoothly
readable - and eagerly expected by many - analysis of the gravity-like
states found in both major twistorial pictures for N=4 super Yang-Mills,
pictures due to Witten and Berkovits, respectively. The reader is supposed
to be familiar with the basic statements of this twistor-Yang-Mills story,
otherwise the text below will be useless for her. The following PowerPoint
XP (more precisely, PowerString PX+i\hbar) file may be useful:
http://schwinger.harvard.edu/~motl/twistors.ppt
First of all, unlike many others, Berkovits and Witten treat these
conformal gravity states as a problem - something that potentially hurts
the exact relation with the N=4 super Yang-Mills S-matrix, and they
present some evidence - one might perhaps say a proof - that the loop
diagrams are damaged by the intermediate gravity states indeed, at the end
of their article, and therefore the twistorial string theories disagree
with Yang-Mills theory at the loop level.
(I fully sympathize with this "critical" approach. As you know, I don't
believe that one can construct a meaningful quantum theory of gravity
starting from the conformal gravity and making a few small steps - this
would indeed be a counterexample to the principle that string theory is
the only theory of quantum gravity. These theories are not theories
containing meaningful gravity, because of the presence of ghosts, and they
also don't seem to be exactly Yang-Mills because the spectrum has these
conformal gravity exotics.)
Nevertheless they compute many details about the gauge-singlets appearing
in these twistor pictures. The effective action described by these new
singlet states, a topic that they study in depth, has inevitably the
superconformal symmetry, inherited from the geometry of the supertwistor
space. This implies that the highest-helicity bosonic part's kinetic terms
must be of the form (Weyl tensor squared). Although it is a problematic
action due to the appearance of ghosts (negative-norm states, much like in
a scalar "\phi box squared \phi" theories which is equivalent to TWO scalar
fields with the OPPOSITE signs of the kinetic terms), many steps, such as
the separation to the self-dual and the anti-self-dual piece, follow in
analogy with the gauge theory case. Just the number of indices is doubled
- four spinor indices, describing helicities between -2 and +2.
The extra gravity states look like volume-preserving vector fields on the
twistor space, or something along these lines, and an extra B-field
provides us with the opposite helicity states. Various details are studied
in the spacetime picture, Berkovits' model, Witten's model, or some
combination of the three.
The Minkowski spacetime translation generator is found to be
non-diagonalizable (Jordan blocks generalizing the nilpotent matrices)
which is an example how these theories break unitarity. The spectrum of
the (multiplet of the) theory has excitations with helicities between -2
and +2; their precise composition looks unusual.
Berkovits and Witten compute the three-point functions and MHV tree
amplitudes, and compare them with Witten's B-model. These are somewhat
less familiar than the gauge theory case, but they may be interesting.
I was happy to see various technical details to be written in a way that I
agree with - for example Nathan now agreed that on the Euclidean
worldsheet of his string, the twistors are complex, and they're only
constrained to be real on the worldsheet's boundary - much like in
Neitzke-Vafa, in a sense.
In the final section 7 they study potential restrictions on the gauge
group. Although I have not absorbed all the details, there is some
possibility to derive the Berkovits' constraint c=28 in the B-model, too,
although the gauge groups on both sides are different. Witten's B-model
would seem to allow U(28), for example, while products of U(1) and SU(2)
current algebras at various levels are discussed on Berkovits' side. It
seems to me that Berkovits' and Witten's pictures are not quite equivalent
either, and the overall story (at least so far) certainly looks less
beautiful than the derivation of the two possible type I gauge groups in
ten dimensions (namely SO(32) and E_8\times E_8).
If I tried to make some conclusions, I would say that the present paper
might invalidate the exact map between the twistorial string theories and
the Yang-Mills S-matrix at the quantum (loop) level, which may imply that
the agreement at the tree level is something that may be guaranteed by
symmetries. This would mean that the twistorial string theories, and their
detailed technical features and differences in particular, are not
terribly fundamental - assuming that the N=4 gauge theory as we know it
*is* fundamental. Nevertheless the tree-level S-matrix of exotic theories
such as the conformal supergravity seems to have a comparably efficient
description in terms of the supertwistor space, which may be interesting
at least for those who think that conformal supergravity theories are
important.
So far, I can still imagine that the twistorial framework offers new,
very different and very efficient tools to calculate the loop amplitudes -
using very different integrals than those over the loop momenta - but it
now seems unlikely that these loop amplitudes are what one would derive in
the most straightforward and controllable ways from the twistor-string
theories that have been presented.
Different points of view are more than welcome.
All the best
Lubos
__{_______________________________________________ _____________________________}
E-mail: lumo@matfyz.cz fax: +1-617/496-0110 Web: http://lumo.matfyz.cz/
eFax: +1-801/454-1858 work: +1-617/496-8199 home: +1-617/868-4487 (call)
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^
[Posted for the 2nd time because of continuing problems with the FAS
newsserver. LM]
Thomas Dent
Jun8-04, 06:48 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Lubos Motl <motl@feynman.harvard.edu> wrote\n\n> Well, today I vote for Berkovits and Witten\n> http://www.arxiv.org/abs/hep-th/0406051\n\nNot a hard decision!\n\n> that the loop\n> diagrams are damaged by the intermediate gravity states indeed, at the end\n> of their article, and therefore the twistorial string theories disagree\n> with Yang-Mills theory at the loop level.\n\nIt would be strange if two different string theories *both*\ncorresponded with N=4 SYM. As you said, where is Maldacena in all of\nthis? (Sitting at strong coupling, I suppose.)\n\n> If I tried to make some conclusions, I would say that the present paper\n> might invalidate the exact map between the twistorial string theories and\n> the Yang-Mills S-matrix at the quantum (loop) level, which may imply that\n> the agreement at the tree level is something that may be guaranteed by\n> symmetries. This would mean that the twistorial string theories, and their\n> detailed technical features and differences in particular, are not\n> terribly fundamental - assuming that the N=4 gauge theory as we know it\n> *is* fundamental.\n\nYou mean accidental or anomalous symmetries that only work at tree\nlevel?\n\nContinuing on the subject "paper of the day", what about Berkovits\ntoday:\n\n"A super-Poincare covariant prescription is then given for the\ncomputation of N-point multiloop amplitudes. One can easily prove that\nmassless N-point multiloop amplitudes vanish for N<4, confirming the\nperturbative finiteness of superstring theory. One can also prove the\nType IIB S-duality conjecture that \\$R^4\\$ terms in the effective action\nreceive no perturbative contributions above one loop."\n\nThis sounds important, but I am not in a position to judge. Is it?\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>Lubos Motl <motl@feynman.harvard.edu> wrote
> Well, today I vote for Berkovits and Witten
> http://www.arxiv.org/abs/http://www.arxiv.org/abs/hep-th/0406051
Not a hard decision!
> that the loop
> diagrams are damaged by the intermediate gravity states indeed, at the end
> of their article, and therefore the twistorial string theories disagree
> with Yang-Mills theory at the loop level.
It would be strange if two different string theories *both*
corresponded with N=4 SYM. As you said, where is Maldacena in all of
this? (Sitting at strong coupling, I suppose.)
> If I tried to make some conclusions, I would say that the present paper
> might invalidate the exact map between the twistorial string theories and
> the Yang-Mills S-matrix at the quantum (loop) level, which may imply that
> the agreement at the tree level is something that may be guaranteed by
> symmetries. This would mean that the twistorial string theories, and their
> detailed technical features and differences in particular, are not
> terribly fundamental - assuming that the N=4 gauge theory as we know it
> *is* fundamental.
You mean accidental or anomalous symmetries that only work at tree
level?
Continuing on the subject "paper of the day", what about Berkovits
today:
"A super-Poincare covariant prescription is then given for the
computation of N-point multiloop amplitudes. One can easily prove that
massless N-point multiloop amplitudes vanish for N<4, confirming the
perturbative finiteness of superstring theory. One can also prove the
Type IIB S-duality conjecture that $R^4$ terms in the effective action
receive no perturbative contributions above one loop."
This sounds important, but I am not in a position to judge. Is it?
Thomas
Lubos Motl
Jun8-04, 11:54 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>On Tue, 8 Jun 2004, Thomas Dent wrote:\n\n> Not a hard decision!\n\nI think that it would be harder today. As far as I see, the contenders\nwould be:\n\n1. Cumrun Vafa\'s paper\nhttp://www.arxiv.org/abs/hep-th/0406058\n\nthat explains the recent Strominger-Vafa-Ooguri statement\nZ_{BH} = |Z_{top}|^2 as two factors coming from two boundaries\nof AdS2, and it relates these theories to 2-dimensional Yang-Mills.\nCumrun can relate many different things and miracles that have appeared\nin the past - like Gross+Taylor\'s derivation of the stringy face\nof two-dimensional Yang-Mills theory, and how it\'s related to\nattractors and charged black holes, and Melvin-like Universes, if you\nallow me to use my language.\n\n2. Nathan Berkovits\' paper\nhttp://www.arxiv.org/abs/hep-th/0406055\n\nthat uses his pure spinor formalism for the superstring to derive\nvarious vanishing theorems for the superstring amplitudes. Concerning\nyour question about the importance of this paper: I think that if\nhe does everything he says ;-), then his formalism is really powerful\nand useful. The statements that he derives have been generally believed\nto be true essentially by everyone in the field, and many of them\nderived in various more or less direct ways, so they won\'t impress\ntoo many people, but the fact that Nathan\'s seemingly weird and\nconvoluted model can do such things is impressive. What I would like to\nsee is whether he can really treat well the Ramond-Ramond backgrounds,\nlike those in the AdS/CFT correspondence; the Green-Schwarz based\nLagrangian should be appropriate for such tasks.\n\n3. T. Padmanabhan\'s new solution of the cosmological constant problem\nhttp://www.arxiv.org/abs/hep-th/0406060\n\nthat advocates that the vacuum energy density scale must be the geometric\naverage of the current Hubble scale and the Planck scale - a popular\ncoincidence of many well-known physicists - and makes some\nsemi-anthropic arguments based on the paradigm that gravity only sees\nthe fluctuations of vacuum energy (?). I have not read it so far, so\nthe new statements of him remain clouded in mystery for me.\n\n4. Matlock and Viswanathan\nhttp://www.arxiv.org/abs/hep-th/0406061\n\nwho extend the correspondence between the BMN operators and excited\nstrings in pp-waves up to 4 impurities (so far it\'s been done for 3\nat most) - cannot one just make a proof for *all* numbers of\nimpurities?\n\n5. Shahin Sheikh-Jabbari and Sergey Prokushin\nhttp://www.arxiv.org/abs/hep-th/0406053\n\nhave a paper on bound states of giant gravitons which become\ndeformed/squashed "giants" (three-spheres) because of the B-field\n\n6. Marshakov has something to say about (semiclassical) AdS/CFT\nintegrability\nhttp://www.arxiv.org/abs/hep-th/0406056\n\nI am sure that other papers are interesting, too, but 6 is enough for a\nlist.\n\n> It would be strange if two different string theories *both*\n> corresponded with N=4 SYM.\n\nYes, I agree.\n\n> As you said, where is Maldacena in all of\n> this? (Sitting at strong coupling, I suppose.)\n\nDo you mean "What Juan says about twistors?" or "How do we see the AdS/CFT\ncorrespondence?" At any rate, I don\'t know the answer to either of these\nquestions.\n\n> You mean accidental or anomalous symmetries that only work at tree\n> level?\n\nSomething analogous - yes, the agreement might be a tree level coincidence\nmuch like various accidental symmetries that only work in some\napproximation.\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 Tue, 8 Jun 2004, Thomas Dent wrote:
> Not a hard decision!
I think that it would be harder today. As far as I see, the contenders
would be:
1. Cumrun Vafa's paper
http://www.arxiv.org/abs/http://www.arxiv.org/abs/hep-th/0406058
that explains the recent Strominger-Vafa-Ooguri statement
Z_{BH} = |Z_{top}|^2 as two factors coming from two boundaries
of AdS2, and it relates these theories to 2-dimensional Yang-Mills.
Cumrun can relate many different things and miracles that have appeared
in the past - like Gross+Taylor's derivation of the stringy face
of two-dimensional Yang-Mills theory, and how it's related to
attractors and charged black holes, and Melvin-like Universes, if you
allow me to use my language.
2. Nathan Berkovits' paper
http://www.arxiv.org/abs/http://www.arxiv.org/abs/hep-th/0406055
that uses his pure spinor formalism for the superstring to derive
various vanishing theorems for the superstring amplitudes. Concerning
your question about the importance of this paper: I think that if
he does everything he says ;-), then his formalism is really powerful
and useful. The statements that he derives have been generally believed
to be true essentially by everyone in the field, and many of them
derived in various more or less direct ways, so they won't impress
too many people, but the fact that Nathan's seemingly weird and
convoluted model can do such things is impressive. What I would like to
see is whether he can really treat well the Ramond-Ramond backgrounds,
like those in the AdS/CFT correspondence; the Green-Schwarz based
Lagrangian should be appropriate for such tasks.
3. T. Padmanabhan's new solution of the cosmological constant problem
http://www.arxiv.org/abs/http://www.arxiv.org/abs/hep-th/0406060
that advocates that the vacuum energy density scale must be the geometric
average of the current Hubble scale and the Planck scale - a popular
coincidence of many well-known physicists - and makes some
semi-anthropic arguments based on the paradigm that gravity only sees
the fluctuations of vacuum energy (?). I have not read it so far, so
the new statements of him remain clouded in mystery for me.
4. Matlock and Viswanathan
http://www.arxiv.org/abs/http://www.arxiv.org/abs/hep-th/0406061
who extend the correspondence between the BMN operators and excited
strings in pp-waves up to 4 impurities (so far it's been done for 3
at most) - cannot one just make a proof for *all* numbers of
impurities?
5. Shahin Sheikh-Jabbari and Sergey Prokushin
http://www.arxiv.org/abs/http://www.arxiv.org/abs/hep-th/0406053
have a paper on bound states of giant gravitons which become
deformed/squashed "giants" (three-spheres) because of the B-field
6. Marshakov has something to say about (semiclassical) AdS/CFT
integrability
http://www.arxiv.org/abs/http://www.arxiv.org/abs/hep-th/0406056
I am sure that other papers are interesting, too, but 6 is enough for a
list.
> It would be strange if two different string theories *both*
> corresponded with N=4 SYM.
Yes, I agree.
> As you said, where is Maldacena in all of
> this? (Sitting at strong coupling, I suppose.)
Do you mean "What Juan says about twistors?" or "How do we see the AdS/CFT
correspondence?" At any rate, I don't know the answer to either of these
questions.
> You mean accidental or anomalous symmetries that only work at tree
> level?
Something analogous - yes, the agreement might be a tree level coincidence
much like various accidental symmetries that only work in some
approximation.
__{_______________________________________________ _____________________________}
E-mail: lumo@matfyz.cz fax: +1-617/496-0110 Web: http://lumo.matfyz.cz/
eFax: +1-801/454-1858 work: +1-617/496-8199 home: +1-617/868-4487 (call)
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Urs Schreiber
Jun8-04, 01:43 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>"Lubos Motl" <motl@feynman.harvard.edu> schrieb im Newsbeitrag\nnews:Pine.LNX.4.31.0406081138410.2316 2-100000@feynman.harvard.edu...\n\n> 2. Nathan Berkovits\' paper\n> http://www.arxiv.org/abs/hep-th/0406055\n>\n> that uses his pure spinor formalism for the superstring to derive\n> various vanishing theorems for the superstring amplitudes. Concerning\n> your question about the importance of this paper: I think that if\n> he does everything he says ;-), then his formalism is really powerful\n> and useful. The statements that he derives have been generally believed\n> to be true essentially by everyone in the field, and many of them\n> derived in various more or less direct ways, so they won\'t impress\n> too many people, but the fact that Nathan\'s seemingly weird and\n> convoluted model can do such things is impressive.\n\nDoes this proof show that all superstring higher-loop diagrams are finite or\neven furthermore that the entire perturbation series converges?\n\nThat seems like a big accomplishment, considering how much work D\'Hoker and\nPhong needed in order to understand 2 loops:\n\nEric D\'Hoker & D.H. Phong\nLectures on two-loop superstrings,\nhep-th/0211111.\n\nwhich is a summary of the series of papers\n\nEric D\'Hoker & D.H. Phong,\nTwo-loop superstrings: I, The main formulas,\nhep-th/0110247.\n\nEric D\'Hoker & D.H. Phong,\nTwo-loop superstrings: II, The chiral measure on moduli space,\nhep-th/0110283.\n\nEric D\'Hoker & D.H. Phong,\nTwo-loop superstrings: III, Slice independence and absence of ambiguities,\nhep-th/0111016.\n\nEric D\'Hoker & D.H. Phong,\nTwo-loop superstrings: IV, The cosmological constant and modular forms,\nhep-th/0111040\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>"Lubos Motl" <motl@feynman.harvard.edu> schrieb im Newsbeitrag
news:Pine.LNX.4.31.0406081138410.23162-100000@feynman.harvard.edu...
> 2. Nathan Berkovits' paper
> http://www.arxiv.org/abs/http://www.arxiv.org/abs/hep-th/0406055
>
> that uses his pure spinor formalism for the superstring to derive
> various vanishing theorems for the superstring amplitudes. Concerning
> your question about the importance of this paper: I think that if
> he does everything he says ;-), then his formalism is really powerful
> and useful. The statements that he derives have been generally believed
> to be true essentially by everyone in the field, and many of them
> derived in various more or less direct ways, so they won't impress
> too many people, but the fact that Nathan's seemingly weird and
> convoluted model can do such things is impressive.
Does this proof show that all superstring higher-loop diagrams are finite or
even furthermore that the entire perturbation series converges?
That seems like a big accomplishment, considering how much work D'Hoker and
Phong needed in order to understand 2 loops:
Eric D'Hoker & D.H. Phong
Lectures on two-loop superstrings,
http://www.arxiv.org/abs/hep-th/0211111.
which is a summary of the series of papers
Eric D'Hoker & D.H. Phong,
Two-loop superstrings: I, The main formulas,
http://www.arxiv.org/abs/hep-th/0110247.
Eric D'Hoker & D.H. Phong,
Two-loop superstrings: II, The chiral measure on moduli space,
http://www.arxiv.org/abs/hep-th/0110283.
Eric D'Hoker & D.H. Phong,
Two-loop superstrings: III, Slice independence and absence of ambiguities,
http://www.arxiv.org/abs/hep-th/0111016.
Eric D'Hoker & D.H. Phong,
Two-loop superstrings: IV, The cosmological constant and modular forms,
http://www.arxiv.org/abs/hep-th/0111040
Just out of curiosity(without killing the cat!) how does a 4-D space gravity, function in a 11-D space-time?
To trace out a Gravitational history form 4-D to 11-D cannot have the same paramiters, and cannot by definition be Gravity?
How soon will there be a Super-Space to accomodate the Super-Gravity?
This is not a being critical to Ed, but I note the paper earlier from him that altered the timescale of (theorized) Proton Decay by a number of magnitude orders, I wonder if this was a 'pre-calculated' exercise with the intention of accomodating obvious problems of Super-String worldline issue's being focused by the wider Scientific community?
PS, I read the above paper at the rate of words per minute equal to '950wpm', I am not sure if I read it at a lower rate, say '2wpm' if it would be more beneficial, but that just me.
Lubos Motl
Jun9-04, 08:33 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>On Tue, 8 Jun 2004, Urs Schreiber wrote:\n\n> Does this proof show that all superstring higher-loop diagrams are finite or\n> even furthermore that the entire perturbation series converges?\n\nNo, it does not. Have I said something like that? Nathan\'s paper is about\nvanishing theorems, i.e. it proves the fact that some special amplitudes -\nsuch as those that calculate the R^4 terms in the IIB effective action,\nor massless 1-, 2-, 3-point amplitudes, receive no contributions from\nmulti-loop diagrams. As far as I see, you are the only person who speaks\nabout a general amplitude.\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 Tue, 8 Jun 2004, Urs Schreiber wrote:
> Does this proof show that all superstring higher-loop diagrams are finite or
> even furthermore that the entire perturbation series converges?
No, it does not. Have I said something like that? Nathan's paper is about
vanishing theorems, i.e. it proves the fact that some special amplitudes -
such as those that calculate the R^4 terms in the IIB effective action,
or massless 1-, 2-, 3-point amplitudes, receive no contributions from
multi-loop diagrams. As far as I see, you are the only person who speaks
about a general amplitude.
__{_______________________________________________ _____________________________}
E-mail: lumo@matfyz.cz fax: +1-617/496-0110 Web: http://lumo.matfyz.cz/
eFax: +1-801/454-1858 work: +1-617/496-8199 home: +1-617/868-4487 (call)
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Urs Schreiber
Jun9-04, 09:20 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>"Lubos Motl" <motl@feynman.harvard.edu> schrieb im Newsbeitrag\nnews:Pine.LNX.4.31.0406090830100.2425 6-100000@feynman.harvard.edu...\n> On Tue, 8 Jun 2004, Urs Schreiber wrote:\n>\n> > Does this proof show that all superstring higher-loop diagrams are\nfinite or\n> > even furthermore that the entire perturbation series converges?\n>\n> No, it does not. Have I said something like that?\n\nNo, but I thought this was the meaning of what Nathan Berkovits writes in\nthe last sentence of the first paragraph of section 6.2:\n\n"[...] these non-renormalization theorems imply that superstring scattering\namplitudes are finite order-by-order in perturbation theory."\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>"Lubos Motl" <motl@feynman.harvard.edu> schrieb im Newsbeitrag
news:Pine.LNX.4.31.0406090830100.24256-100000@feynman.harvard.edu...
> On Tue, 8 Jun 2004, Urs Schreiber wrote:
>
> > Does this proof show that all superstring higher-loop diagrams are
finite or
> > even furthermore that the entire perturbation series converges?
>
> No, it does not. Have I said something like that?
No, but I thought this was the meaning of what Nathan Berkovits writes in
the last sentence of the first paragraph of section 6.2:
"[...] these non-renormalization theorems imply that superstring scattering
amplitudes are finite order-by-order in perturbation theory."
Nathan Berkovits
Jun9-04, 11:36 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>On Wed, 9 Jun 2004, Urs Schreiber wrote:\n\n> No, but I thought this was the meaning of what Nathan Berkovits writes in\n> the last sentence of the first paragraph of section 6.2:\n>\n> "[...] these non-renormalization theorems imply that superstring scattering\n> amplitudes are finite order-by-order in perturbation theory."\n\nHi Urs, Lubos, and folks,\n\nYes, assuming factorization and assuming that there are no additional\nsources to unphysical divergences which come in the interior of moduli\nspace. In conformally invariant theories, there are no obvious sources for\nsuch divergences (but they could come from contact terms in light-cone\ngauge theories). There is some discussion of the relation between the\nnonrenorm theorems and finiteness in the paper of Martinec.\n\nRegards, Nathan\n\n[Moderator\'s note: My guess is that Nathan means this paper: LM]\n\nhttp://www-spires.slac.stanford.edu/spires/find/hep/www?rawcmd=find+a+martinec+and+title+finiteness&FORMAT=WWW\nhttp://www-spires.slac.stanford.edu/spires/fi\nnd/hep/www?rawcmd=find+a+martinec+and+title+finiteness&FORMAT=WWW\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>On Wed, 9 Jun 2004, Urs Schreiber wrote:
> No, but I thought this was the meaning of what Nathan Berkovits writes in
> the last sentence of the first paragraph of section 6.2:
>
> "[...] these non-renormalization theorems imply that superstring scattering
> amplitudes are finite order-by-order in perturbation theory."
Hi Urs, Lubos, and folks,
Yes, assuming factorization and assuming that there are no additional
sources to unphysical divergences which come in the interior of moduli
space. In conformally invariant theories, there are no obvious sources for
such divergences (but they could come from contact terms in light-cone
gauge theories). There is some discussion of the relation between the
nonrenorm theorems and finiteness in the paper of Martinec.
Regards, Nathan
[Moderator's note: My guess is that Nathan means this paper: LM]
http://www-spires.slac.stanford.edu/spires/find/hep/www?rawcmd=find+a+martinec+and+title+finiteness&FORMAT=WWW
http://www-spires.slac.stanford.edu/spires/fi
nd/hep/www?rawcmd=find+a+martinec+and+title+finiteness&FORMAT=WWW
Thomas Dent
Jun9-04, 02:50 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>Lubos Motl <motl@feynman.harvard.edu> wrote\n\n> 2. Nathan Berkovits\' paper\n> http://www.arxiv.org/abs/hep-th/0406055\n>\n> that uses his pure spinor formalism for the superstring to derive\n> various vanishing theorems for the superstring amplitudes. Concerning\n> your question about the importance of this paper: I think that if\n> he does everything he says ;-), then his formalism is really powerful\n> and useful. The statements that he derives have been generally believed\n> to be true essentially by everyone in the field, and many of them\n> derived in various more or less direct ways (...)\n\nDo you have some references (apart from the odyssey of D\'Hoker and\nPhong) for derivations of the vanishing theorems? Everyone would like\nthem to be true, but that does not constitute a proof.\n\n> 3. T. Padmanabhan\'s new solution of the cosmological constant problem\n> http://www.arxiv.org/abs/hep-th/0406060\n>\n> that advocates that the vacuum energy density scale must be the geometric\n> average of the current Hubble scale and the Planck scale - a popular\n> coincidence of many well-known physicists - and makes some\n> semi-anthropic arguments based on the paradigm that gravity only sees\n> the fluctuations of vacuum energy (?).\n\nClouded in mystery for me too. It is an unusual paper in that the\nnumber of pages is a variable, r. (Unsurprisingly, r turns out to take\nthe value 4.) Given the Einstein equation with T_mu nu defined as\nusual, the statement that you have placed (?) next to makes no sense.\nBut if we accept it, there appears to be a phenomenological problem in\nthat the vacuum energy he gets is *always* M_P^2H^2, thus it seems\ndifficult to get the right decelerating behaviour in the early\nUniverse. Also the equation of state is doubtful.\n\nI don\'t see how it is so very different from the \'holographic\'\nconsiderations pioneered by Cohen, Kaplan and Nelson in\nhttp://www.arxiv.org/abs/hep-th/9803132 . (For an update of why this\ndoesn\'t work as a dark energy model, see S.D. Hsu\nhttp://www.arxiv.org/abs/hep-th/0403052 .)\n\nHow many solutions does the cosmological constant problem need? (Ans.:\none solution that works!)\n\n> I am sure that other papers are interesting, too, but 6 is enough for a\n> list.\n\nParticularly for someone working on leptogenesis and fermion mass\ntextures.\n\nIncidentally, the "new" posting apparently from me on "string theory\nand experimental practice" was made via physicsforums.com about 1 week\nago!\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
> 2. Nathan Berkovits' paper
> http://www.arxiv.org/abs/http://www.arxiv.org/abs/hep-th/0406055
>
> that uses his pure spinor formalism for the superstring to derive
> various vanishing theorems for the superstring amplitudes. Concerning
> your question about the importance of this paper: I think that if
> he does everything he says ;-), then his formalism is really powerful
> and useful. The statements that he derives have been generally believed
> to be true essentially by everyone in the field, and many of them
> derived in various more or less direct ways (...)
Do you have some references (apart from the odyssey of D'Hoker and
Phong) for derivations of the vanishing theorems? Everyone would like
them to be true, but that does not constitute a proof.
> 3. T. Padmanabhan's new solution of the cosmological constant problem
> http://www.arxiv.org/abs/http://www.arxiv.org/abs/hep-th/0406060
>
> that advocates that the vacuum energy density scale must be the geometric
> average of the current Hubble scale and the Planck scale - a popular
> coincidence of many well-known physicists - and makes some
> semi-anthropic arguments based on the paradigm that gravity only sees
> the fluctuations of vacuum energy (?).
Clouded in mystery for me too. It is an unusual paper in that the
number of pages is a variable, r. (Unsurprisingly, r turns out to take
the value 4.) Given the Einstein equation with T_{mu} \nu defined as
usual, the statement that you have placed (?) next to makes no sense.
But if we accept it, there appears to be a phenomenological problem in
that the vacuum energy he gets is *always* M_P^2H^2, thus it seems
difficult to get the right decelerating behaviour in the early
Universe. Also the equation of state is doubtful.
I don't see how it is so very different from the 'holographic'
considerations pioneered by Cohen, Kaplan and Nelson in
http://www.arxiv.org/abs/http://www.arxiv.org/abs/hep-th/9803132 . (For an update of why this
doesn't work as a dark energy model, see S.D. Hsu
http://www.arxiv.org/abs/http://www.arxiv.org/abs/hep-th/0403052 .)
How many solutions does the cosmological constant problem need? (Ans.:
one solution that works!)
> I am sure that other papers are interesting, too, but 6 is enough for a
> list.
Particularly for someone working on leptogenesis and fermion mass
textures.
Incidentally, the "new" posting apparently from me on "string theory
and experimental practice" was made via physicsforums.com about 1 week
ago!
Urs Schreiber
Jun9-04, 02:55 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 Wed, 9 Jun 2004, Thomas Dent wrote:\n\n> Incidentally, the "new" posting apparently from me on "string theory\n> and experimental practice" was made via physicsforums.com about 1 week\n> ago!\n\n[Moderator\'s note: Yes, but it only appeared this morning on our\nmoderator\'s account - together with a bunch of other posts from\nPhysicsForums, most of them from last week at least. I am guessing that\nthis still has to do with the problems with the newsserver at Harvard.\n-usc]]\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>On Wed, 9 Jun 2004, Thomas Dent wrote:
> Incidentally, the "new" posting apparently from me on "string theory
> and experimental practice" was made via physicsforums.com about 1 week
> ago!
[Moderator's note: Yes, but it only appeared this morning on our
moderator's account - together with a bunch of other posts from
PhysicsForums, most of them from last week at least. I am guessing that
this still has to do with the problems with the newsserver at Harvard.
-usc]]
Thomas Larsson
Jun14-04, 11:40 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Lubos Motl <motl@feynman.harvard.edu> wrote in message news:<20040607043457.C2574@mail.kolej.mff.cuni.cz> ...\n\n> Well, today I vote for Berkovits and Witten\n>\n> http://www.arxiv.org/abs/hep-th/0406051\n>\n> If I tried to make some conclusions, I would say that the present paper\n> might invalidate the exact map between the twistorial string theories and\n> the Yang-Mills S-matrix at the quantum (loop) level, which may imply that\n> the agreement at the tree level is something that may be guaranteed by\n> symmetries.\n\nI was under the impression that the main point with the twistor\nstring was that it gave you a more efficient way to evaluate\namplitudes in super Yang-Mills theory. Isn\'t it a problem if\ntwistor techniques give you the wrong answer?\n\n[Moderator\'s note: I think that it is clearly a problem for various\nspecific far-reaching conjectures about equivalences including the\nquantum corrections, but I also believe that unlike\nyou, string theorists also have different and more important\ntasks than to look for problems. ;-) Well, of course, if\nsomething is proved wrong in physics, we just immediately\ntreat it as something proved wrong. It\'s a YES/NO question,\nand I have no emotional preference among these two answers. LM]\n\n> This would mean that the twistorial string theories, and their\n> detailed technical features and differences in particular, are not\n> terribly fundamental - assuming that the N=4 gauge theory as we know it\n> *is* fundamental. Nevertheless the tree-level S-matrix of exotic theories\n> such as the conformal supergravity seems to have a comparably efficient\n> description in terms of the supertwistor space, which may be interesting\n> at least for those who think that conformal supergravity theories are\n> important.\n\nYour post seems to indicate that you are not entirely convinced about\nthe importance of conformal supergravity (lack of unitarity because of\nfourth-order equations of motion, etc.). So is this still interesting\nfor you?\n\n[Moderator\'s note: Your conclusion is correct, the continued\nresearch in the direction of conformal SUGRA is not too\ninteresting for me, but it may be more important whether it\nis interesting for others. Let me also assure you that the\nimportance and depth of some specific constructions based\non twistor is not the most essential question about science.\nI think that are many interesting open challenges and chances\nassociated with twistors and with instanton expansions in\ngeneral. 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>Lubos Motl <motl@feynman.harvard.edu> wrote in message news:<20040607043457.C2574@mail.kolej.mff.cuni.cz>...
> Well, today I vote for Berkovits and Witten
>
> http://www.arxiv.org/abs/http://www.arxiv.org/abs/hep-th/0406051
>
> If I tried to make some conclusions, I would say that the present paper
> might invalidate the exact map between the twistorial string theories and
> the Yang-Mills S-matrix at the quantum (loop) level, which may imply that
> the agreement at the tree level is something that may be guaranteed by
> symmetries.
I was under the impression that the main point with the twistor
string was that it gave you a more efficient way to evaluate
amplitudes in super Yang-Mills theory. Isn't it a problem if
twistor techniques give you the wrong answer?
[Moderator's note: I think that it is clearly a problem for various
specific far-reaching conjectures about equivalences including the
quantum corrections, but I also believe that unlike
you, string theorists also have different and more important
tasks than to look for problems. ;-) Well, of course, if
something is proved wrong in physics, we just immediately
treat it as something proved wrong. It's a YES/NO question,
and I have no emotional preference among these two answers. LM]
> This would mean that the twistorial string theories, and their
> detailed technical features and differences in particular, are not
> terribly fundamental - assuming that the N=4 gauge theory as we know it
> *is* fundamental. Nevertheless the tree-level S-matrix of exotic theories
> such as the conformal supergravity seems to have a comparably efficient
> description in terms of the supertwistor space, which may be interesting
> at least for those who think that conformal supergravity theories are
> important.
Your post seems to indicate that you are not entirely convinced about
the importance of conformal supergravity (lack of unitarity because of
fourth-order equations of motion, etc.). So is this still interesting
for you?
[Moderator's note: Your conclusion is correct, the continued
research in the direction of conformal SUGRA is not too
interesting for me, but it may be more important whether it
is interesting for others. Let me also assure you that the
importance and depth of some specific constructions based
on twistor is not the most essential question about science.
I think that are many interesting open challenges and chances
associated with twistors and with instanton expansions in
general. LM]
Urs Schreiber
Jun17-04, 05:52 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>On Wed, 9 Jun 2004, Nathan Berkovits wrote:\n\n> On Wed, 9 Jun 2004, Urs Schreiber wrote:\n>\n> > No, but I thought this was the meaning of what Nathan Berkovits writes in\n> > the last sentence of the first paragraph of section 6.2:\n> >\n> > "[...] these non-renormalization theorems imply that superstring scattering\n> > amplitudes are finite order-by-order in perturbation theory."\n\n> Yes, assuming factorization and assuming that there are no additional\n> sources to unphysical divergences which come in the interior of moduli\n> space. In conformally invariant theories, there are no obvious sources for\n> such divergences (but they could come from contact terms in light-cone\n> gauge theories).\n\n\nOver at his blog Peter Woit says\n(http://www.math.columbia.edu/~woit/mt/mt-comments.cgi?entry_id=37) that he\nhas talked with D\'Hoker and Phong about the above mentioned paper and that\nhe got the impression that they tend to think that the disappearance of\nthe unphysical divergences in the interior of moduli space would be the\nhard part of a proof.\n\nHe writes:\n\n> I don\'t want to speak for D\'Hoker and Phong, but this is my probably\n> somewhat garbled understanding from having discussed this with both of\n> them:\n>\n> Berkovits\'s claim of finiteness explicitly assumes "there are no\n> unphysical divergences in the interior of moduli space". This assumption\n> (that these divergences cancel) is exactly what is hard to prove in the\n> two-loop case and no one knows how to do for higher loops. In conformal\n> gauge Berkovits argues that "there are no obvious potential sources for\n> these unphysical divergences in the interior of moduli space since the\n> amplitudes are independent (up to surface terms) of the locations of\n> picture-changing operators." D\'Hoker and Phong have found that the\n> correct definition of picture-changing operators is quite subtle here.\n> These are operator products at a point and their definition is\n> ambiguous. To make them well-defined in a\n> way that is gauge invariant requires understanding some global terms.\n> Unless you do this you don\'t have well-defined picture-changing\n> operators and can get whatever answer you want.\n>\n> Again, I\'m obviously not an expert at this, but that is my understanding\n> of what the experts told me. While I don\'t want to speak for them, from\n> what they told me I am under the strong impression that these experts\n> don\'t believe that Berkovits has a proof.\n\n\nI don\'t quite understand if the above mentioned possible problem with\ndefining the picture changing operators is the same one or is different\nfrom that discussed by Nathan Berkovits on p. 14 of hep-th/0406055, where\nit says:\n\n"Up to possible surface terms, the amplitudes are independent of the\nworldsheet positions of [the picure changing operators] since the\nworldsheet derivatives of the picture changing operators are\nBRST-trivial. [...]\n\n"If the correlation function diverges near the boundary of moduli space,\nthese surface terms can give finite contributions which need to be\ntreated carefully. [...]"\n\n"However, since the correlation functions in this formalism do not\ndiverge near the boudnary of moduli space, there are no subtleties due to\nsurface terms."\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>On Wed, 9 Jun 2004, Nathan Berkovits wrote:
> On Wed, 9 Jun 2004, Urs Schreiber wrote:
>
> > No, but I thought this was the meaning of what Nathan Berkovits writes in
> > the last sentence of the first paragraph of section 6.2:
> >
> > "[...] these non-renormalization theorems imply that superstring scattering
> > amplitudes are finite order-by-order in perturbation theory."
> Yes, assuming factorization and assuming that there are no additional
> sources to unphysical divergences which come in the interior of moduli
> space. In conformally invariant theories, there are no obvious sources for
> such divergences (but they could come from contact terms in light-cone
> gauge theories).
Over at his blog Peter Woit says
(http://www.math.columbia.edu/~woit/mt/mt-comments.cgi?entry_id=37) that he
has talked with D'Hoker and Phong about the above mentioned paper and that
he got the impression that they tend to think that the disappearance of
the unphysical divergences in the interior of moduli space would be the
hard part of a proof.
He writes:
> I don't want to speak for D'Hoker and Phong, but this is my probably
> somewhat garbled understanding from having discussed this with both of
> them:
>
> Berkovits's claim of finiteness explicitly assumes "there are no
> unphysical divergences in the interior of moduli space". This assumption
> (that these divergences cancel) is exactly what is hard to prove in the
> two-loop case and no one knows how to do for higher loops. In conformal
> gauge Berkovits argues that "there are no obvious potential sources for
> these unphysical divergences in the interior of moduli space since the
> amplitudes are independent (up to surface terms) of the locations of
> picture-changing operators." D'Hoker and Phong have found that the
> correct definition of picture-changing operators is quite subtle here.
> These are operator products at a point and their definition is
> ambiguous. To make them well-defined in a
> way that is gauge invariant requires understanding some global terms.
> Unless you do this you don't have well-defined picture-changing
> operators and can get whatever answer you want.
>
> Again, I'm obviously not an expert at this, but that is my understanding
> of what the experts told me. While I don't want to speak for them, from
> what they told me I am under the strong impression that these experts
> don't believe that Berkovits has a proof.
I don't quite understand if the above mentioned possible problem with
defining the picture changing operators is the same one or is different
from that discussed by Nathan Berkovits on p. 14 of http://www.arxiv.org/abs/hep-th/0406055, where
it says:
"Up to possible surface terms, the amplitudes are independent of the
worldsheet positions of [the picure changing operators] since the
worldsheet derivatives of the picture changing operators are
BRST-trivial. [...]
"If the correlation function diverges near the boundary of moduli space,
these surface terms can give finite contributions which need to be
treated carefully. [...]"
"However, since the correlation functions in this formalism do not
diverge near the boudnary of moduli space, there are no subtleties due to
surface terms."
vBulletin® v3.7.6, Copyright ©2000-2009, Jelsoft Enterprises Ltd.