Holographic Aspects of Non-minimal $R_{\mu \alpha \nu \beta } F^{(a)\mu \alpha } F^{(a)\nu \beta } $ AdS Black Brane

TL;DR

This paper explores the holographic dual of an Einstein-Yang-Mills black brane with non-minimal coupling, deriving new solutions and calculating physical properties like conductivity and viscosity ratios.

Contribution

It constructs a first-order non-minimal coupling black hole solution and computes the DC conductivity and shear viscosity to entropy density ratio, revealing new insights into holographic models.

Findings

Shear viscosity to entropy density ratio saturates the KSS bound.

First-order non-minimal coupling affects the conductivity.

New results for conductivity at first order in coupling.

Abstract

In this paper, we study the holographic dual to an asymptotically anti-de Sitter black brane in an Einstein-Yang-Mills model with a non-minimal coupling between the Riemann and Yang-Mills fields. First, we construct a planar black hole solution of this model up to the first order of the non-minimal coupling of the Yang-Mills field with the Riemann-Christoffel tensor, denoted as $q_2$. Then, we calculate the color non-abelian direct current (DC) conductivity and the ratio of shear viscosity to entropy density for this solution. Our result for the shear viscosity $\eta$ to entropy density $s$ ratio saturates the Kovtun, Son, and Starinets (KSS) bound, which is proportional to $\frac{1}{4 \pi}$. However, our result for the conductivity is new up to the first order of $q_2$.