Shear Viscosity of Strongly Coupled N = 4 Supersymmetric Yang-Mills Plasma

Using the anti–de Sitter/conformal field theory correspondence, we relate the shear viscosity η 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 η = π/8N²T³. We conjecture that for finite ’t Hooft coupling g_YM²N the shear viscosity is η = f(g_YM²N)N²T³, where f(x) is a monotonic function that decreases from O(x^-2ln^-1(1/x)) at small x to π/8 when x→∞.