Hydrodynamic fluctuations, long-time tails, and supersymmetry

By P. Kovtun, Laurence G. Yaffe. 2003

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Hydrodynamic fluctuations at non-zero 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 wavenumber, 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.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/76472bf446ea31a1480bdc4712ce88a293bee9a1

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Citations in the corpus

Lectures on hydrodynamic fluctuations in relativistic theories (2012, methodology): “Following [45, 24], we will evaluate the effect of the nonlinear terms in the hydrodynamic equations on the correlation functions of spatial currents Ji and stresses T i j in the hydrodynamic regime ω → 0 and k → 0.”
Holography and hydrodynamics: Diffusion on stretched horizons (2003, background): “Long-time, long-distance behavior in this theory is governed by conventional hydrodynamics,6 with hydrodynamic variables being just densities (6)For systematic discussion of hydrodynamic fluctuations in supersymmetric theories, see [15].”
Pseudogap and time reversal breaking in a holographic superconductor (2008, background): “Perhaps such cuts reaching ω = 0 are suppressed at large N in a similar manner to those resulting in hydrodynamic tails [29].”
Coupling constant dependence of the shear viscosity in N=4 supersymmetric Yang–Mills theory (2004, background): “Shear viscosity of N = 4 SYM from supergravity Shear viscosity is the transport coefficient that appears in the hydrodynamic constitutive relation for the spatial components of the stress-energy tensor (see [21], [31] for more hydrodynamics preliminaries).”
Lectures on holographic methods for condensed matter physics (2009, background): “Indeed, the suppression of power law tails at large N was seen at weak coupling in [83].”
Quasinormal modes and holography (2005, background): “Of course, this simple nature of singularities is only possible at infinite Nc; for example, it is known that low-energy correlation functions of conserved currents develop branch cuts in the complex frequency plane, with discontinuities across the cuts suppressed in the Nc→∞ limit (such cuts are no”