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Hydrodynamic fluctuations, long-time tails, and supersymmetry

Hydrodynamic fluctuations, long-time tails, and supersymmetry Hydrodynamic fluctuations at a nonzero temperature can cause slow relaxation toward equilibrium even in observables which are not locally conserved. A classic example is the stress-stress correlator in a normal fluid, which, at zero wave number, behaves at large times as t - 3 / 2 . A novel feature of the effective theory of hydrodynamic fluctuations in supersymmetric theories is the presence of Grassmann-valued classical fields describing macroscopic supercharge density fluctuations. We show that hydrodynamic fluctuations in supersymmetric theories generate essentially the same long-time power-law tails in real-time correlation functions that are known in simple fluids. In particular, a t - 3 / 2 long-time tail must exist in the stress-stress correlator of N = 4 supersymmetric Yang-Mills theory at non-zero temperature, regardless of the value of the coupling. Consequently, this feature of finite-temperature dynamics can provide an interesting test of the AdS/CFT correspondence. However, the coefficient of this long-time tail is suppressed by a factor of 1 / N c 2 . On the gravitational side, this implies that these long-time tails are not present in the classical supergravity limit; they must instead be produced by one-loop gravitational fluctuations. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Physical Review D American Physical Society (APS)

Hydrodynamic fluctuations, long-time tails, and supersymmetry

Kovtun, Pavel; Yaffe, Laurence G
Physical Review D , Volume 68 (2) – Jul 15, 2003
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Publisher
American Physical Society (APS)
Copyright
Copyright © 2003 The American Physical Society
ISSN
1089-4918
DOI
10.1103/PhysRevD.68.025007
Publisher site
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Abstract

Hydrodynamic fluctuations at a nonzero temperature can cause slow relaxation toward equilibrium even in observables which are not locally conserved. A classic example is the stress-stress correlator in a normal fluid, which, at zero wave number, behaves at large times as t - 3 / 2 . A novel feature of the effective theory of hydrodynamic fluctuations in supersymmetric theories is the presence of Grassmann-valued classical fields describing macroscopic supercharge density fluctuations. We show that hydrodynamic fluctuations in supersymmetric theories generate essentially the same long-time power-law tails in real-time correlation functions that are known in simple fluids. In particular, a t - 3 / 2 long-time tail must exist in the stress-stress correlator of N = 4 supersymmetric Yang-Mills theory at non-zero temperature, regardless of the value of the coupling. Consequently, this feature of finite-temperature dynamics can provide an interesting test of the AdS/CFT correspondence. However, the coefficient of this long-time tail is suppressed by a factor of 1 / N c 2 . On the gravitational side, this implies that these long-time tails are not present in the classical supergravity limit; they must instead be produced by one-loop gravitational fluctuations.

Journal

Physical Review D – American Physical Society (APS)

Published: Jul 15, 2003

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