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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 ηof 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/8 N^2T^3. We conjecture that for finite 't Hooft coupling (g_YM)^2N the shear viscosity is η=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 π/8 when x\to\infty.