Hydrodynamics from the D1-brane

TL;DR

This paper calculates the bulk viscosity to entropy density ratio in strongly coupled 1+1 dimensional SU(N) Yang-Mills theory using gauge/gravity duality, finding it to be universally 1/4π across various D1-brane backgrounds.

Contribution

It demonstrates that the bulk viscosity to entropy density ratio is universally 1/4π for a class of 1+1 dimensional theories dual to D1-brane gravitational backgrounds.

Findings

The ratio of bulk viscosity to entropy density is 1/4π.

This ratio is consistent across different D1-brane backgrounds.

The result applies to theories dual to D1-branes at cones over Sasaki-Einstein 7-manifolds.

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 1/4\pi. This ratio continues to be $1/4\pi$ 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 1/4\pi 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.