Hydrodynamics from the D1-brane

TL;DR

The paper addresses hydrodynamics of a 1+1 dimensional SU(N) gauge theory realized on D1-branes at finite temperature via gauge/gravity duality. By analyzing the sound-channel quasinormal mode in the gravity dual and matching to general hydrodynamic expectations, it computes the bulk viscosity to entropy density ratio, finding $\xi/s = 1/4\pi$ in the relevant non-conformal regime. The result is corroborated by a Kubo-formula calculation and shown to persist for the F1-string dual and for D1-branes at Sasaki-Einstein cones, suggesting a universal value across a class of 1+1D gravity duals. The work also provides a general equation for the diff-invariant sound mode in a 3D Einstein-dilaton system, enabling broader applicability to related holographic theories and potential extensions to charged or deformed D1/D5 setups.

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 1/4πfor 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.