Universal hydrodynamics of non-conformal branes

TL;DR

This paper uses holography to relate the hydrodynamics of non-conformal branes to conformal hydrodynamics, deriving explicit relations for transport coefficients and viscosity ratios based on higher-dimensional AdS solutions.

Contribution

It demonstrates that non-conformal brane hydrodynamics can be derived from conformal cases via dimensional reduction, providing explicit second-order stress tensor forms and viscosity ratios.

Findings

Hydrodynamics of non-conformal branes is fully determined by conformal hydrodynamics.

Derived the ratio of bulk to shear viscosity as a function of sound speed and dimension.

Predicted the second-order non-conformal hydrodynamic stress tensor form.

Abstract

We examine the hydrodynamic limit of non-conformal branes using the recently developed precise holographic dictionary. We first streamline the discussion of holography for backgrounds that asymptote locally to non-conformal brane solutions by showing that all such solutions can be obtained from higher dimensional asymptotically locally AdS solutions by suitable dimensional reduction and continuation in the dimension. As a consequence, many holographic results for such backgrounds follow from the corresponding results of the Asymptotically AdS case. In particular, the hydrodynamics of non-conformal branes is fully determined in terms of conformal hydrodynamics. Using previous results on the latter we predict the form of the non-conformal hydrodynamic stress tensor to second order in derivatives. Furthermore we show that the ratio between bulk and shear viscosity is fixed by the generalized conformal structure to be \zeta/\eta = 2(1/(d-1) - c_s^2), where c_s is the speed of sound in the fluid.