Hydrodynamics from the Dp-brane

TL;DR

This work computes hydrodynamic transport coefficients for the plasmas dual to stacks of non-extremal Dp-branes in the decoupling limit ($p=2$–$6$), including a new expression for the bulk viscosity. Using a consistent $p+2$-dimensional gravity-scalar reduction and gauge-invariant fluctuations, the authors derive dispersion relations in shear and sound channels, obtaining $rac{η}{s}=rac{1}{4\pi}$, $v_s^2=rac{5-p}{9-p}$, and $rac{ζ}{η}=rac{2(3-p)^2}{p(9-p)}$, with the compact relation $rac{ζ}{η}=-2igl(v_s^2-rac{1}{p}igr)$. The analysis confirms frame-independence of the results and discusses holographic renormalization via minimal counterterms. The findings extend the universality of holographic transport to non-conformal backgrounds and connect to prior work on little string theories and compactified D4-branes.

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 ζ/η= -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.