Holographic Aspects of Non-minimal $R^3 F^2 $ Black Brane in an EFT Framework

TL;DR

This paper explores a modified gravity theory with non-minimal R^3 F^2 coupling, deriving black brane solutions and analyzing how this affects holographic transport coefficients like conductivity and shear viscosity.

Contribution

It introduces a first-order corrected black brane solution in an EFT framework with non-minimal R^3 F^2 coupling and examines its impact on holographic transport properties.

Findings

Non-minimal coupling modifies DC conductivity and shear viscosity ratios.

Positive q_2 violates the conductivity bound.

Negative q_2 violates the KSS viscosity bound.

Abstract

This work investigates a modified theory of gravity where the Einstein-Hilbert action, including a cosmological constant, is non-minimally coupled to a Yang-Mills field via an \(R^3 F_{\mu \alpha}^{(a)} F^{(a)\mu \alpha}\) interaction term. We treat this coupling as the leading higher-derivative correction in a low-energy effective field theory (EFT) deformation of the standard Einstein-Yang-Mills theory. We derive a black brane solution for this model, accurate to the first order in the EFT coupling parameter \(q_2\), and specify the regime of validity \(\frac{|q_2|}{L^6} \ll 1\). Using gauge/gravity duality techniques, we then compute two key holographic transport coefficients: the color non-abelian direct current (DC) conductivity and the ratio of shear viscosity to entropy density. Our analysis reveals that both transport coefficients are modified by the non-minimal coupling, with the conductivity bound violated for positive \(q_2\) and the Kovtun-Son-Starinets (KSS) bound for shear viscosity violated for negative \(q_2\). The results are interpreted within the EFT framework, and possible constraints on the sign of \(q_2\) from stability and causality are discussed. In the limit where the non-minimal coupling vanishes, our results consistently reduce to those of the standard Yang-Mills Schwarzschild Anti-de Sitter (AdS) black brane.