Strings on AdS2 and the highenergy limit of noncritical Mtheory
Abstract
Abstract. Noncritical Mtheory in 2+1 dimensions has been defined as a doublescaling limit of a nonrelativistic Fermi liquid on a flat twodimensional plane. Here we study this noncritical Mtheory in the limit of high energies, analogous to the alpha' > infinity limit of string theory. In the related case of twodimensional Type 0A strings, it has been argued that the conformal alpha' > infinity limit leads to AdS_2 with a propagating fermion whose mass is set by the value of the RR flux. Here we provide evidence that in the highenergy limit, the natural ground state of noncritical Mtheory similarly describes the AdS_2 x S1 spacetime, with a massless propagating fermion. We argue that the spacetime effective theory in this background is captured by a topological higherspin extension of conformal ChernSimons gravity in 2+1 dimensions, consistently coupled to a massless Dirac field. Intriguingly, the twodimensional plane populated by the original nonrelativistic fermions is essentially the twistor space associated with the symmetry group of the AdS_2 x S1 spacetime; thus, at least in the highenergy limit, noncritical Mtheory can be nonperturbatively described as a"Fermi liquid on twistor space.''
 Authors:
 Publication Date:
 Research Org.:
 Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
 Sponsoring Org.:
 Physics Division
 OSTI Identifier:
 934677
 Report Number(s):
 LBNL401E
TRN: US0803825
 DOE Contract Number:
 DEAC0205CH11231
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Journal of High Energy Physics; Journal Volume: 2007; Journal Issue: 06; Related Information: Journal Publication Date: 06/11/2007
 Country of Publication:
 United States
 Language:
 English
 Subject:
 72; DIMENSIONS; FERMI GAS; FERMIONS; GROUND STATES; SPACETIME; SYMMETRY GROUPS; Bosonic Strings; MTheory; Gaugegravity correspondence
Citation Formats
Horava, Petr, Horava, Petr, and Keeler, Cynthia A. Strings on AdS2 and the highenergy limit of noncritical Mtheory. United States: N. p., 2007.
Web. doi:10.1088/11266708/2007/06/031.
Horava, Petr, Horava, Petr, & Keeler, Cynthia A. Strings on AdS2 and the highenergy limit of noncritical Mtheory. United States. doi:10.1088/11266708/2007/06/031.
Horava, Petr, Horava, Petr, and Keeler, Cynthia A. Mon .
"Strings on AdS2 and the highenergy limit of noncritical Mtheory". United States.
doi:10.1088/11266708/2007/06/031. https://www.osti.gov/servlets/purl/934677.
@article{osti_934677,
title = {Strings on AdS2 and the highenergy limit of noncritical Mtheory},
author = {Horava, Petr and Horava, Petr and Keeler, Cynthia A.},
abstractNote = {Abstract. Noncritical Mtheory in 2+1 dimensions has been defined as a doublescaling limit of a nonrelativistic Fermi liquid on a flat twodimensional plane. Here we study this noncritical Mtheory in the limit of high energies, analogous to the alpha' > infinity limit of string theory. In the related case of twodimensional Type 0A strings, it has been argued that the conformal alpha' > infinity limit leads to AdS_2 with a propagating fermion whose mass is set by the value of the RR flux. Here we provide evidence that in the highenergy limit, the natural ground state of noncritical Mtheory similarly describes the AdS_2 x S1 spacetime, with a massless propagating fermion. We argue that the spacetime effective theory in this background is captured by a topological higherspin extension of conformal ChernSimons gravity in 2+1 dimensions, consistently coupled to a massless Dirac field. Intriguingly, the twodimensional plane populated by the original nonrelativistic fermions is essentially the twistor space associated with the symmetry group of the AdS_2 x S1 spacetime; thus, at least in the highenergy limit, noncritical Mtheory can be nonperturbatively described as a"Fermi liquid on twistor space.''},
doi = {10.1088/11266708/2007/06/031},
journal = {Journal of High Energy Physics},
number = 06,
volume = 2007,
place = {United States},
year = {Mon Apr 16 00:00:00 EDT 2007},
month = {Mon Apr 16 00:00:00 EDT 2007}
}

It is shown that, in the theory of free noncritical strings, there are no modularinvariant partition functions on surfaces of higher genus. This is due to the fact that the vacuum expectation value of the stressenergy tensor is singular in the fundamental region on the complex plane in which Riemann surfaces are mapped. The above singularity is associated with a nonzero vacuum expectation value of the 2Dgravity field. 15 refs.



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