Holographic renormalization and anisotropic black branes in higher curvature gravity

TL;DR

This paper constructs an analytic, anisotropic black brane solution in five-dimensional Gauss-Bonnet gravity, explores its holographic properties, and computes physical quantities like shear viscosity and conductivities for the dual plasma.

Contribution

It introduces a non-perturbative in Gauss-Bonnet coupling, analytic anisotropic black brane solution with holographic renormalization, and physical property calculations for the dual plasma.

Findings

Analytic black brane solution with anisotropy in higher curvature gravity

Holographic renormalization of anisotropic plasma with two central charges

Computed shear viscosity to entropy ratio and conductivities

Abstract

We consider five-dimensional AdS-axion-dilaton gravity with a Gauss-Bonnet term and find a solution of the equations of motion which corresponds to a black brane exhibiting a spatial anisotropy, with the source of the anisotropy being an axion field linear in one of the horizon coordinates. Our solution is static, regular everywhere on and outside the horizon, and asymptotically AdS. It is analytic and valid in a small anisotropy expansion, but fully non-perturbative in the Gauss-Bonnet coupling. We discuss various features of this solution and use it as a gravity dual to a strongly coupled anisotropic plasma with two independent central charges, $a\neq c$. In the limit of small Gauss-Bonnet coupling, we carry out holographic renormalization of the system using (a recursive variant of) the Hamilton-Jacobi method and derive a generic expression for the boundary stress tensor, which we later specialize to our solution. Finally, we compute the shear viscosity to entropy ratios and conductivities of this anisotropic plasma.