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Urs Schreiber
Jul15-04, 06:00 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>Yesterday Hermann Nicolai, together with Axel Kleinschmidt, came out with\nnew facts\n\nH. Nicolai & A. Kleinschmidt\nE10 and SO(9,9) invariant supergravity,\nhep-th/0407101\n\nabout the relation between supergravity and the coset E10/K(E10), which we\nhave discussed here before\n\nhttp://groups.google.de/groups?selm=Pine.LNX.4.31.0404171914110.5742-100000%40feynman.harvard.edu\n\nhttp://golem.ph.utexas.edu/string/archives/000353.html .\n\nI haven\'t read it yet, but the point seems to be that they refine their\ncomparison of sugra degreees of freedom with those in the first couple of\nlevels (in a decomposition by SL(10,R) reps) of the sigma model on\nexp(E10/K(E10)) by now explicitly studying the dimensional reduction of\nvarious sugra flavors to 1 dimension.\n\nThey claim to find new hidden SO(9,9) symmetries in the reduced theory\n(related to T-duality) and now repeat the previous level expansion but now\nwith respect to a decomposiiton of E10 with respect to this SO(9,9)\n\nThey say that some of these SO(9,9) reps are spinorial, namely those at odd\nlevel, while the vector reps appear at even levels. This can apparently be\nidentified with the R-R and the NS-NS sectors, respectively.\n\nI find it very interesting that now also fermionic degrees of sugra are\ntaken into account, even though only at level 0. The 1+0 dimensional susy\nsigma model actions of the reduced sugra are explicitly given, but they say\nthat "even the most basic aspects of the fermionic sector in relation to the\nhyperbolic symmetry remain to be understood." (p.2).\n\nAn attempt by Englert and HGuoart to show how the E10 conjecture hangs\ntogether with P. West\'s work on E11 is mentioned, which I had missed before,\nit is given in hep-th/0402076, hep-th/0405082.\n\nThe very intersting work hep-th/0401053 by Brown, Ganor and Helfgott is\nmentioned, but it is apparently not directly relevant or related to the\nSO(9,9) decomposition business.\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">&nbsp;&nbsp;View this Usenet post in original ASCII form </a></div><P></jabberwocky>Yesterday Hermann Nicolai, together with Axel Kleinschmidt, came out with
new facts

H. Nicolai & A. Kleinschmidt
E10 and SO(9,9) invariant supergravity,
http://www.arxiv.org/abs/hep-th/0407101

about the relation between supergravity and the coset E10/K(E10), which we
have discussed here before

http://groups.google.de/groups?selm=Pine.LNX.4.31.0404171914110.5742-100000%40feynman.harvard.edu

http://golem.ph.utexas.edu/string/archives/000353.html .

I haven't read it yet, but the point seems to be that they refine their
comparison of sugra degreees of freedom with those in the first couple of
levels (in a decomposition by SL(10,R) reps) of the \sigma model on
\exp(E10/K(E10)) by now explicitly studying the dimensional reduction of
various sugra flavors to 1 dimension.

They claim to find new hidden SO(9,9) symmetries in the reduced theory
(related to T-duality) and now repeat the previous level expansion but now
with respect to a decomposiiton of E10 with respect to this SO(9,9)

They say that some of these SO(9,9) reps are spinorial, namely those at odd
level, while the vector reps appear at even levels. This can apparently be
identified with the R-R and the NS-NS sectors, respectively.

I find it very interesting that now also fermionic degrees of sugra are
taken into account, even though only at level . The 1+0 dimensional susy
\sigma model actions of the reduced sugra are explicitly given, but they say
that "even the most basic aspects of the fermionic sector in relation to the
hyperbolic symmetry remain to be understood." (p.2).

An attempt by Englert and HGuoart to show how the E10 conjecture hangs
together with P. West's work on E11 is mentioned, which I had missed before,
it is given in http://www.arxiv.org/abs/hep-th/0402076, http://www.arxiv.org/abs/hep-th/0405082.

The very intersting work http://www.arxiv.org/abs/hep-th/0401053 by Brown, Ganor and Helfgott is
mentioned, but it is apparently not directly relevant or related to the
SO(9,9) decomposition business.

Urs Schreiber
Jul15-04, 02:37 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>"Urs Schreiber" &lt;Urs.Schreiber@uni-essen.de&gt; schrieb im Newsbeitrag\nnews:2ln6d7Fen2ojU1-100000@uni-berlin.de...\n&gt; Yesterday Hermann Nicolai, together with Axel Kleinschmidt, came out with\n&gt; new facts\n&gt;\n&gt; H. Nicolai & A. Kleinschmidt\n&gt; E10 and SO(9,9) invariant supergravity,\n&gt; hep-th/0407101\n\nIt is intersting how this sugra&lt;-&gt;Kac-Moody thing can be studied in various\ndimensions. Let d be the number of dimensions that D=11 sugra is\ndimensionally reduced to, then we have\n\nd = 2 &lt;-&gt; E9\n\nd= 1 &lt;-&gt; E10\n\nd=0 &lt;-&gt; E11 (?) .\n\nIn another recent paper\n\nH. Nicolai & H. Samtleben:\nOn K(E9)\nhep-th/0407055\n\nthe d=2 case is further examined, which goes back (at least) to\n\nH. Nicolai & H. Samtleben:\nIntegrability and Canonical Structure of d=2, N=16 Supergravity,\nhep-th/9804152 .\n\nIf we allow to freely associate then this looks intriguing, because in this\ncase we are now dealing with a worldsheet theory, which smells of strings.\nBut that would be too weird to be exactly true, and as emphasized in this\npaper, it is not. The highest susy for a super_conformal_ QFT in 2d is\napparently N=4.\n\nN=16 is the highest susy in 2d in general, obtained from reducing D=11 sugra\nto 2 dimensions. The authors say that N=16 sugra this is the "most\nsymmetric" QFT in 2 dimensions.\n\nIn any case, d=2, N=16 sugra is not conformal, due to a worldsheet dilaton.\nAlso, the constraint algebra has structure functions instead of structure\nconstants.\n\n&gt;From a quick glance over that paper I could not fully figure out how the E9\nsymmetry appears.\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">&nbsp;&nbsp;View this Usenet post in original ASCII form </a></div><P></jabberwocky>"Urs Schreiber" <Urs.Schreiber@uni-essen.de> schrieb im Newsbeitrag
news:2ln6d7Fen2ojU1-100000@uni-berlin.de...
> Yesterday Hermann Nicolai, together with Axel Kleinschmidt, came out with
> new facts
>
> H. Nicolai & A. Kleinschmidt
> E10 and SO(9,9) invariant supergravity,
> http://www.arxiv.org/abs/hep-th/0407101

It is intersting how this sugra<->Kac-Moody thing can be studied in various
dimensions. Let d be the number of dimensions that D=11 sugra is
dimensionally reduced to, then we have

d = 2 <-> E9d= 1 <-> E10

d=0 <-> E11 (?) .

In another recent paper

H. Nicolai & H. Samtleben:
On K(E9)
http://www.arxiv.org/abs/hep-th/0407055

the d=2 case is further examined, which goes back (at least) to

H. Nicolai & H. Samtleben:
Integrability and Canonical Structure of d=2, N=16 Supergravity,
http://www.arxiv.org/abs/hep-th/9804152 .

If we allow to freely associate then this looks intriguing, because in this
case we are now dealing with a worldsheet theory, which smells of strings.
But that would be too weird to be exactly true, and as emphasized in this
paper, it is not. The highest susy for a super_conformal_ QFT in 2d is
apparently N=4.

N=16 is the highest susy in 2d in general, obtained from reducing D=11 sugra
to 2 dimensions. The authors say that N=16 sugra this is the "most
symmetric" QFT in 2 dimensions.

In any case, d=2, N=16 sugra is not conformal, due to a worldsheet dilaton.
Also, the constraint algebra has structure functions instead of structure
constants.

>From a quick glance over that paper I could not fully figure out how the E9
symmetry appears.