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

TL;DR

This paper computes the leading coupling correction to the shear viscosity and the viscosity-to-entropy ratio η/s in N=4 SYM using α'-corrections to type IIB supergravity. By perturbing the α'-corrected near-extremal black three-brane background and evaluating the real-time retarded correlator via the Minkowski AdS/CFT prescription, the authors derive η = (π/8) N_c^2 T^3 [1 + (75/4) ζ(3) (g^2_{YM} N_c)^{-3/2} + …] and η/s = (1/4π) [1 + (135/8) ζ(3) (g^2_{YM} N_c)^{-3/2} + …]. The corrections are positive, extending the Kovtun–Son–Starinets bound to the next order in the strong coupling expansion. The work confirms the robustness of the η/s = 1/(4π) baseline and provides the first finite-coupling correction for this theory. The analysis leverages the α'-corrected background, a careful treatment of higher-derivative boundary terms, and the Minkowski AdS/CFT framework for real-time correlators.

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 πN_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 α'-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 1/4πin the limit of infinite coupling). The correction to 1/4πscales as (g^2_{YM} N_c)^{-3/2} with a positive coefficient.