Hydrodynamics from the D1-brane

Abstract

We study the hydrodynamic properties of strongly coupled SU(N) Yang-Mills theory of the D1-brane at finite temperature in the framework of gauge/gravity duality. The only non-trivial viscous transport coefficient in 1+1 dimensions is the bulk viscosity. We evaluate the bulk viscosity by isolating the quasi-normal mode corresponding to the sound channel for the gravitational background of the D1-brane. We find that the ratio of the bulk viscosity to the entropy density to be 1/4π . This ratio continues to be 1/4π also in the regime when the D1-brane Yang-Mills theory is dual to the gravitational background of the fundamental string. Our analysis shows that this ratio is equal to 1/4π for a class of gravitational backgrounds dual to field theories in 1+1 dimensions obtained by considering D1-branes at cones over Sasaki-Einstein 7-manifolds.