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

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 $\frac{\mathrm{\mid }{q}_2\mathrm{\mid }}{L^6}\ll 1$. 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.