Higher Derivative Corrections to Locally Black Brane Metrics

TL;DR

This work addresses how higher-derivative corrections in the bulk, specifically Gauss-Bonnet terms with coefficient $α'$, modify holographic hydrodynamics in the dual CFT. By extending the fluid/gravity derivative expansion to include $α'$ corrections, the authors solve the $α'$-corrected Einstein equations to first order in boundary derivatives, construct the corrected bulk metric, and compute the holographic boundary stress tensor via holographic renormalization, obtaining explicit $α'$-dependent transport data. They find that the shear viscosity and entropy density receive $α'$-dependent corrections and reproduce the well-known result $η/s = rac{1}{4π}igl(1 - rac{8 α'}{L^2}igr)$, with all expressions consistent with previous methods. The results validate a systematic framework for incorporating higher-derivative gravity into AdS/CFT hydrodynamics and set the stage for extending the analysis to higher orders and other higher-derivative terms such as $R^4$.

Abstract

In this paper we generalize the construction of locally boosted black brane space time to higher derivative gravities. We consider the Gauss-Bonnet term (with coefficient $α'$) as a toy example. We find the solution to the $α'$ corrected Einstein equations to first order in the boundary derivative expansion. This allows us to find the $α'$ corrections to the boundary stress tensor in the presence of the Gauss-Bonnet term in the bulk action. We therefore obtain the ratio of shear viscosity to entropy which agrees with other methods of computation in the literature.