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Title: Quantum critical transport, duality, and M theory

Abstract

We consider charge transport properties of 2+1 dimensional conformal field theories at nonzero temperature. For theories with only Abelian U(1) charges, we describe the action of particle-vortex duality on the hydrodynamic-to-collisionless crossover function: this leads to powerful functional constraints for self-dual theories. For N=8 supersymmetric, SU(N) Yang-Mills theory at the conformal fixed point, exact hydrodynamic-to-collisionless crossover functions of the SO(8) R-currents can be obtained in the large N limit by applying the anti-de Sitter/conformal field theory (AdS/CFT) correspondence to M theory. In the gravity theory, fluctuating currents are mapped to fluctuating gauge fields in the background of a black hole in 3+1 dimensional anti-de Sitter space. The electromagnetic self-duality of the 3+1 dimensional theory implies that the correlators of the R-currents obey a functional constraint similar to that found from particle-vortex duality in 2+1 dimensional Abelian theories. Thus the 2+1 dimensional, superconformal Yang Mills theory obeys a 'holographic self-duality' in the large N limit, and perhaps more generally.

Authors:
 [1];  [2];  [3];  [4]
  1. Department of Physics, University of Washington, Seattle, Washington 98195-1560 (United States)
  2. Kavli Institute for Theoretical Physics, University of California, Santa Barbara, California 93106-4030 (United States)
  3. Department of Physics, Harvard University, Cambridge Massachusetts 02138 (United States)
  4. Institute for Nuclear Theory, University of Washington, Seattle, Washington 98195-1550 (United States)
Publication Date:
OSTI Identifier:
21020432
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. D, Particles Fields; Journal Volume: 75; Journal Issue: 8; Other Information: DOI: 10.1103/PhysRevD.75.085020; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; BLACK HOLES; CHARGE TRANSPORT; CONFORMAL INVARIANCE; DE SITTER GROUP; DUALITY; GRAVITATION; HOLOGRAPHY; M-THEORY; QUANTUM FIELD THEORY; SO GROUPS; SU GROUPS; SUPERSYMMETRY; U-1 GROUPS; VORTICES; YANG-MILLS THEORY

Citation Formats

Herzog, Christopher P., Kovtun, Pavel, Sachdev, Subir, and Son, Dam Thanh. Quantum critical transport, duality, and M theory. United States: N. p., 2007. Web. doi:10.1103/PHYSREVD.75.085020.
Herzog, Christopher P., Kovtun, Pavel, Sachdev, Subir, & Son, Dam Thanh. Quantum critical transport, duality, and M theory. United States. doi:10.1103/PHYSREVD.75.085020.
Herzog, Christopher P., Kovtun, Pavel, Sachdev, Subir, and Son, Dam Thanh. Sun . "Quantum critical transport, duality, and M theory". United States. doi:10.1103/PHYSREVD.75.085020.
@article{osti_21020432,
title = {Quantum critical transport, duality, and M theory},
author = {Herzog, Christopher P. and Kovtun, Pavel and Sachdev, Subir and Son, Dam Thanh},
abstractNote = {We consider charge transport properties of 2+1 dimensional conformal field theories at nonzero temperature. For theories with only Abelian U(1) charges, we describe the action of particle-vortex duality on the hydrodynamic-to-collisionless crossover function: this leads to powerful functional constraints for self-dual theories. For N=8 supersymmetric, SU(N) Yang-Mills theory at the conformal fixed point, exact hydrodynamic-to-collisionless crossover functions of the SO(8) R-currents can be obtained in the large N limit by applying the anti-de Sitter/conformal field theory (AdS/CFT) correspondence to M theory. In the gravity theory, fluctuating currents are mapped to fluctuating gauge fields in the background of a black hole in 3+1 dimensional anti-de Sitter space. The electromagnetic self-duality of the 3+1 dimensional theory implies that the correlators of the R-currents obey a functional constraint similar to that found from particle-vortex duality in 2+1 dimensional Abelian theories. Thus the 2+1 dimensional, superconformal Yang Mills theory obeys a 'holographic self-duality' in the large N limit, and perhaps more generally.},
doi = {10.1103/PHYSREVD.75.085020},
journal = {Physical Review. D, Particles Fields},
number = 8,
volume = 75,
place = {United States},
year = {Sun Apr 15 00:00:00 EDT 2007},
month = {Sun Apr 15 00:00:00 EDT 2007}
}
  • We describe general features of frequency-dependent charge transport near strongly interacting quantum critical points in 2+1 dimensions. The simplest description using the AdS/CFT correspondence leads to a self-dual Einstein-Maxwell theory on AdS{sub 4}, which fixes the conductivity at a frequency-independent self-dual value. We describe the general structure of higher-derivative corrections to the Einstein-Maxwell theory, and compute their implications for the frequency dependence of the quantum critical conductivity. We show that physical consistency conditions on the higher-derivative terms allow only a limited frequency dependence in the conductivity. The frequency dependence is amenable to a physical interpretation using transport of either particlelikemore » or vortexlike excitations.« less
  • We investigate Seiberg{close_quote}s N=1 field theory duality for four-dimensional supersymmetric QCD with the M-theory 5-brane. We find that the M-theory configuration for the magnetic dual theory arises via a smooth deformation of the M-theory configuration for the electric theory. The creation of Dirichlet 4-branes as Neveu-Schwarz 5-branes are passed through each other in type IIA string theory is given an elegant derivation from M theory. {copyright} {ital 1998} {ital The American Physical Society}
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