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 $\hbar=1$), 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 $\sigma = 1 - q_2 \bigl(9\kappa Q^2/(L^2 r_h^4) + 7\kappa^2 Q^4/(4 r_h^8)\bigr)$, 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 $\eta/s = (1/(4\pi))\bigl(1 + q_2\, 7\kappa^2 Q^4/(2 r_h^8)\bigr)$, 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.