Hydrodynamics of Nonminimal $F^{(a)\alpha \beta }{F}^{(a)\gamma \lambda }{R}_{\alpha \gamma }{R}_{\beta \lambda }$ AdS Black Brane

Abstract

We investigate the hydrodynamic properties of a strongly coupled non-Abelian plasma dual to a four-dimensional AdS black brane with a nonminimal coupling of the form $q_2{F}^{(a)\alpha \beta }{F}^{(a)\gamma \lambda }{R}_{\alpha \gamma }{R}_{\beta \lambda }$ in the bulk action. This higher-derivative term introduces a direct interaction between the Yang-Mills field strength and the Ricci tensor, leading to corrections beyond the minimal Einstein-Yang-Mills theory. Using a perturbative expansion in the small coupling $q_2$, we construct the black brane solution up to first order and employ the fluid-gravity correspondence to compute two key transport coefficients: the DC color conductivity $\sigma$ and the shear viscosity to entropy density ratio $\eta /s$. In holography, $\eta /s$ is inversely proportional to the square of the coupling constant of the boundary theory, while $\sigma$ in Einstein-Maxwell theory satisfies a universal lower bound $\sigma \ge 1$ (in units where $\hslash =1$), saturated for uncharged black holes and characterizing a perfect quantum critical fluid. Our results reveal that the nonminimal coupling significantly alters these transport quantities. For the DC conductivity, we find $\sigma =1-q_2(9\kappa Q^2/(L^2{r}_h^4)+7{\kappa }^2{Q}^4/(4r_h^8))$, indicating a violation of the conductivity bound for $q_2>0$ while the bound is preserved for $q_2<0$. For the shear viscosity, we obtain $\eta /s=(1/(4\pi ))(1+q_{2}7{\kappa }^2{Q}^4/(2r_h^8))$, showing that the KSS bound is modified by a term linear in $q_2$. The sign of $q_2$ determines whether the ratio increases above or decreases below the universal value $1/(4\pi )$. These findings highlight the sensitivity of holographic transport to curvature-coupled gauge interactions and provide a controlled example of how higher-derivative corrections influence the hydrodynamic regime of strongly coupled plasmas.

20 pages, no figure