Shear viscosity of strongly coupled N=4 supersymmetric Yang-Mills plasma -: art. no. 081601

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 /8N(2)T(3). We conjecture that for finite 't Hooft coupling g(YM)(2)N the shear viscosity is eta = f(g(YM)(2)N)(NT3)-T-2, 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 --> infinity.