Holographic Aspects of Non-minimal $RF^{(a)}_{\mu \alpha }F^{(a)\mu \alpha} $ Black Brane

TL;DR

This paper explores a modified gravity model with a non-minimal coupling between Ricci scalar and Yang-Mills fields, deriving black brane solutions and analyzing their transport properties, including conductivity and viscosity ratios.

Contribution

It introduces a new gravity theory with Ricci-Yang-Mills coupling and derives black brane solutions up to first order, analyzing their holographic transport properties.

Findings

Derived black brane solutions with non-minimal Ricci-Yang-Mills coupling.

Calculated DC conductivity and shear viscosity to entropy density ratio.

Results recover standard Yang-Mills Schwarzschild AdS black brane in a specific limit.

Abstract

In this paper, we consider Einstein-Hilbert gravity in the presence of cosmological constant and an electric field of Yang-Mills type, which is minimally coupled to gravity. We couple the Ricci scalar to the Yang-Mills invariant to obtain a modified theory of gravity. The black brane solution of this model is introduced up to the first order of the $RF^{(a)}_{\mu \alpha }F^{(a)\mu \alpha} $ term. Then, the color non-abelian direct current (DC) conductivity and the ratio of shear viscosity to entropy density are calculated for this solution. Our results recover the Yang-Mills Schwarzschild AdS black brane in the limit of $q_2 \to 0$.