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Title: Dimensional Duality

Abstract

We show that string theory on a compact negatively curved manifold, preserving a U(1)b1 winding symmetry, grows at least b1 new effective dimensions as the space shrinks. The winding currents yield a ''D-dual'' description of a Riemann surface of genus h in terms of its 2h dimensional Jacobian torus, perturbed by a closed string tachyon arising as a potential energy term in the worldsheet sigma model. D-branes on such negatively curved manifolds also reveal this structure, with a classical moduli space consisting of a b{sub 1}-torus. In particular, we present an AdS/CFT system which offers a non-perturbative formulation of such supercritical backgrounds. Finally, we discuss generalizations of this new string duality.

Authors:
; ; ; ; ; ; ; ; ;
Publication Date:
Research Org.:
Stanford Linear Accelerator Center (SLAC)
Sponsoring Org.:
USDOE
OSTI Identifier:
907709
Report Number(s):
SLAC-PUB-12439
Journal ID: ISSN 0031-9007; PRLTAO; arXiv:0705.0550; TRN: US0703360
DOE Contract Number:
AC02-76SF00515
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review Letters
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; DIMENSIONS; DUALITY; POTENTIAL ENERGY; RIEMANN SHEET; SIGMA MODEL; SYMMETRY; TACHYONS; Theory-HEP,HEPTH

Citation Formats

Green, Daniel, /SLAC /Stanford U., Phys. Dept., Lawrence, Albion, /Brandeis U., McGreevy, John, /MIT, LNS, Morrison, David R., /Duke U., CGTP /UC, Santa Barbara, Silverstein, Eva, and /SLAC /Stanford U., Phys. Dept.. Dimensional Duality. United States: N. p., 2007. Web. doi:10.1103/PhysRevD.76.066004.
Green, Daniel, /SLAC /Stanford U., Phys. Dept., Lawrence, Albion, /Brandeis U., McGreevy, John, /MIT, LNS, Morrison, David R., /Duke U., CGTP /UC, Santa Barbara, Silverstein, Eva, & /SLAC /Stanford U., Phys. Dept.. Dimensional Duality. United States. doi:10.1103/PhysRevD.76.066004.
Green, Daniel, /SLAC /Stanford U., Phys. Dept., Lawrence, Albion, /Brandeis U., McGreevy, John, /MIT, LNS, Morrison, David R., /Duke U., CGTP /UC, Santa Barbara, Silverstein, Eva, and /SLAC /Stanford U., Phys. Dept.. Fri . "Dimensional Duality". United States. doi:10.1103/PhysRevD.76.066004. https://www.osti.gov/servlets/purl/907709.
@article{osti_907709,
title = {Dimensional Duality},
author = {Green, Daniel and /SLAC /Stanford U., Phys. Dept. and Lawrence, Albion and /Brandeis U. and McGreevy, John and /MIT, LNS and Morrison, David R. and /Duke U., CGTP /UC, Santa Barbara and Silverstein, Eva and /SLAC /Stanford U., Phys. Dept.},
abstractNote = {We show that string theory on a compact negatively curved manifold, preserving a U(1)b1 winding symmetry, grows at least b1 new effective dimensions as the space shrinks. The winding currents yield a ''D-dual'' description of a Riemann surface of genus h in terms of its 2h dimensional Jacobian torus, perturbed by a closed string tachyon arising as a potential energy term in the worldsheet sigma model. D-branes on such negatively curved manifolds also reveal this structure, with a classical moduli space consisting of a b{sub 1}-torus. In particular, we present an AdS/CFT system which offers a non-perturbative formulation of such supercritical backgrounds. Finally, we discuss generalizations of this new string duality.},
doi = {10.1103/PhysRevD.76.066004},
journal = {Physical Review Letters},
number = ,
volume = ,
place = {United States},
year = {Fri May 18 00:00:00 EDT 2007},
month = {Fri May 18 00:00:00 EDT 2007}
}
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  • We identify the states in string theory which are responsible for the entropy of near-extremal rotating four-dimensional black holes in {ital N}=8 supergravity. For black holes far from extremality (with no rotation), the Bekenstein-Hawking entropy is exactly matched by a mysterious duality invariant extension of the formulas derived for near-extremal black holes states. {copyright} {ital 1996 The American Physical Society.}
  • In the context of D-dimensional Euclidean gravity, we define the natural generalization to D dimensions of the self-dual Yang-Mills equations as duality conditions on the curvature two-form of a Riemannian manifold. Solutions to these self-duality equations are provided by manifolds of SU(2), SU(3), G{sub 2}, and Spin(7) holonomy. The equations in eight dimensions are a master set for those in lower dimensions. By considering gauge fields propagating on these self-dual manifolds and embedding the spin connection in the gauge connection, solutions to the D-dimensional equations for self-dual Yang-Mills fields are found. We show that the Yang-Mills action on such manifoldsmore » is topologically bounded from below, with the bound saturated precisely when the Yang-Mills field is self-dual. These results have a natural interpretation in supersymmetric string theory. {copyright} {ital 1997} {ital The American Physical Society}« less
  • Duality relations for the two-dimensional nonhomogeneous Ising model on the finite square lattice wrapped on the torus are obtained. The partition function of the model on the dual lattice with arbitrary combinations of the periodical and antiperiodical boundary conditions along the cycles of the torus is expressed through some specific combination of the partition functions of the model on the original lattice with corresponding boundary conditions. It is shown that the structure of the duality relations is connected with the topological peculiarities of the dual transformation of the model on the torus. {copyright} {ital 1997} {ital The American Physical Society}