Hydrodynamics from the Dp-brane

TL;DR

This paper computes viscous transport coefficients, including bulk viscosity, for black Dp-brane geometries in string theory, revealing a universal relation between bulk viscosity and the speed of sound across different p values.

Contribution

It provides the first complete calculation of bulk viscosity for Dp-branes and establishes a simple relation linking bulk viscosity to the speed of sound for p=2,...,6.

Findings

Bulk viscosity is related to shear viscosity and speed of sound by a universal formula.

Shear viscosity is rederived from gravitational perturbations.

The relation ta/ta = -2(v_s^2-1/p) holds for all studied p.

Abstract

We complete the computation of viscous transport coefficients in the near horizon geometries that arise from a stack of black Dp-branes for p=2,...,6 in the decoupling limit. The main new result is the obtention of the bulk viscosity which, for all p, is found to be related to the speed of sound by the simple relation \zeta/\eta = -2(v_s^2-1/p). For completeness the shear viscosity is rederived from gravitational perturbations in the shear and scalar channels. We comment on technical issues like the counterterms needed, or the possible dependence on the conformal frame.