Coupling constant dependence of the shear viscosity in N=4 supersymmetric Yang-Mills theory

Gauge theory-gravity duality predicts that the shear viscosity of N = 4 supersymmetric SU(N-c) Yang-Mills plasma at temperature T in the limit of large N-c and large 't Hooft coupling g(YM)(2) N-c is independent of the coupling and equals to piN(c)(2)T(3)/8. In this paper, we compute the leading correction to the shear viscosity in inverse powers of 't Hooft coupling using the alpha'-corrected low-energy effective action of type IIB string theory. We also find the correction to the ratio of shear viscosity to the volume entropy density (equal to 1/4pi in the limit of infinite coupling). The correction to 1/4pi scales as (g(YM)(2) N-c)(-3/2) with a positive coefficient. (C) 2004 Elsevier B.V. All rights reserved.