Shear viscosity of strongly coupled N=4 supersymmetric Yang-Mills plasma

TL;DR

This paper uses the AdS/CFT correspondence to calculate the shear viscosity of strongly coupled N=4 supersymmetric Yang-Mills plasma, revealing a universal ratio and proposing a dependence on the 't Hooft coupling.

Contribution

It provides an exact calculation of shear viscosity in the strong coupling limit and conjectures its behavior at finite coupling, connecting gravity duals with gauge theory transport properties.

Findings

Shear viscosity ta=pi/8 N^2 T^3 at strong coupling

The absorption cross section of gravitons equals the horizon area in the zero-frequency limit

Proposed a monotonic function describing ta at finite coupling

Abstract

Using the anti-de Sitter/conformal field theory correspondence, we relate the shear viscosity \eta of the finite-temperature N=4 supersymmetric Yang-Mills theory in the large N, strong-coupling regime with the absorption cross section of low-energy gravitons by a near-extremal black three-brane. We show that in the limit of zero frequency this cross section coincides with the area of the horizon. From this result we find \eta=\pi/8 N^2T^3. We conjecture that for finite 't Hooft coupling (g_YM)^2N the shear viscosity is \eta=f((g_YM)^2N) N^2T^3, where f(x) is a monotonic function that decreases from O(x^{-2}\ln^{-1}(1/x)) at small x to \pi/8 when x\to\infty.