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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)T3. We conjecture that for finite 't Hooft coupling g(2)(YM)N the shear viscosity is eta = f(g(2)(YM)N)N2T3, 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

physical review letters

Shear Viscosity of Strongly Coupled<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>N</mml:mi><mml:mspace /><mml:mo>=</mml:mo><mml:mspace /><mml:mn>4</mml:mn><mml:mn /></mml:math>Supersymmetric Yang-Mills Plasma

Shear Viscosity of Strongly CoupledN=4Supersymmetric Yang-Mills Plasma