Holographic Aspects of Non-minimal $R^3 F^{(a)}_{μα}F^{(a)μα} $ Black Brane

TL;DR

The paper addresses holographic transport in a gravity theory endowed with a non-minimal $R^3 F^{(a)}_{\,\mu\nu}F^{(a)\mu\nu}$ coupling to a Yang–Mills field in AdS$_4$. It constructs a black brane solution perturbatively to first order in the coupling $q_2$ and computes two key observables of the dual field theory: the color non-abelian DC conductivity $\sigma^{(33)}_{xx}$ and the shear viscosity to entropy density ratio $\eta/s$, using Green–Kubo and membrane-paradigm techniques, respectively. The results show $\sigma^{(33)}_{xx} = 1 - q_2 R^3(r_h)$ and $\eta/s = \frac{1}{4\pi}[1 + q_2 \mathcal{C}(r_h) + \mathcal{O}(q_2^2)]$, with horizon quantities $R(r_h)$ and $\mathcal{C}(r_h)$. Notably, the conductivity bound is violated for $q_2>0$ and the KSS bound is violated for $q_2<0$, while the $q_2\to 0$ limit recovers the standard Einstein–Yang–Mills AdS values, validating the perturbative approach and highlighting how higher-derivative non-minimal couplings can qualitatively modify holographic transport and bounds.

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 $R^3 F^{(a)}_{μα}F^{(a)μα}$ interaction term. We derive a black brane solution for this model, accurate to the first order in the coupling parameter. 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 $q_2$. 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.