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

TL;DR

The paper analyzes finite-coupling corrections in the strongly coupled ${\cal N}=4$ SYM plasma via the gauge/gravity duality by incorporating leading $\alpha'$ corrections to the type IIB black D3-brane background. Transport coefficients are extracted from the dispersion relations of the lowest quasinormal modes in the corrected geometry, with the result that $\eta/s = \frac{1}{4\pi} (1 + 135 \gamma + O(\gamma^2))$ where $\gamma = \frac{1}{8}\zeta(3) (\alpha')^3$, while the leading corrections to bulk viscosity and the speed of sound vanish: $\zeta = O(\gamma^2)$ and $c_s^2 = \tfrac{1}{3} + O(\gamma^2)$. This provides a nontrivial hydrodynamic consistency check for $\alpha'$-corrected backgrounds and sheds light on the structure of finite-coupling corrections in holographic plasmas.

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.