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(Nc) Yang-Mills plasma at temperature T in the limit of large Nc and large 't Hooft coupling gYM2Nc is independent of the coupling and equals to πNc2T3/8. In this paper, we compute the leading correction to the shear viscosity in inverse powers of 't Hooft coupling using the α′-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 1/4π in the limit of infinite coupling). The correction to 1/4π scales as (gYM2Nc)−3/2 with a positive coefficient.