Transport properties of N=4 supersymmetric Yang-Mills theory at finite coupling

TL;DR

This paper computes finite coupling corrections to transport coefficients in N=4 supersymmetric Yang-Mills theory using gauge/gravity duality, confirming previous shear viscosity results and finding no correction to bulk viscosity or speed of sound.

Contribution

It provides the first calculation of inverse 't Hooft coupling corrections to multiple transport coefficients in N=4 SYM plasma via string theory methods.

Findings

Shear viscosity correction matches previous results.

No correction to bulk viscosity at leading order.

No correction to the speed of sound at leading order.

Abstract

Gauge theory-string theory duality describes strongly coupled N=4 supersymmetric SU(n) Yang-Mills theory at finite temperature in terms of near extremal black 3-brane geometry in type IIB string theory. We use this correspondence to compute the leading correction in inverse 't Hooft coupling to the shear diffusion constant, bulk viscosity and the speed of sound in the large-n N=4 supersymmetric Yang-Mills theory plasma. The transport coefficients are extracted from the dispersion relation for the shear and the sound wave lowest quasinormal modes in the leading order alpha'-corrected black D3 brane geometry. We find the shear viscosity extracted from the shear diffusion constant to agree with result of [hep-th/0406264]; also, the leading correction to bulk viscosity and the speed of sound vanishes. Our computation provides a highly nontrivial consistency check on the hydrodynamic description of the alpha'-corrected nonextremal black branes in string theory.