Coupling constant dependence of the shear viscosity in N=4 supersymmetric Yang-Mills theory

TL;DR

This paper calculates how the shear viscosity of N=4 supersymmetric Yang-Mills plasma varies with the 't Hooft coupling, providing leading corrections to the previously coupling-independent value predicted by gauge/gravity duality.

Contribution

It introduces the first computation of the leading inverse 't Hooft coupling correction to shear viscosity in N=4 SYM using 1-corrected string theory effective action.

Findings

The shear viscosity to entropy density ratio receives positive corrections at finite coupling.

The correction scales as (g^2_{YM} N_c)^{-3/2} and modifies the infinite coupling limit.

The ratio approaches but deviates from 1/47 at finite coupling.

Abstract

Gauge theory - gravity duality predicts that the shear viscosity of N=4 supersymmetric SU(N_c) Yang-Mills plasma at temperature T in the limit of large N_c and large 't Hooft coupling g^2_{YM} N_c is independent of the coupling and equals to \pi N_c^2 T^3/8. In this paper, we compute the leading correction to the shear viscosity in inverse powers of 't Hooft coupling using the \alpha'-corrected low-energy effective action of type IIB string theory. We also find the correction to the ratio of shear viscosity to the volume entropy density (equal to 1/4\pi in the limit of infinite coupling). The correction to 1/4\pi scales as (g^2_{YM} N_c)^{-3/2} with a positive coefficient.