Hydrodynamics of Nonminimal $F^{(a)αβ} F^{(a)γλ} R_{αγ} R_{βλ}$ 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 $q_2 F^{(a)αβ}F^{(a)γλ}R_{αγ}R_{βλ}$ 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 $σ$ and the shear viscosity to entropy density ratio $η/s$. In holography, $η/s$ is inversely proportional to the square of the coupling constant of the boundary theory, while $σ$ in Einstein-Maxwell theory satisfies a universal lower bound $σ\ge 1$ (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 $σ= 1 - q_2 \bigl(9κQ^2/(L^2 r_h^4) + 7κ^2 Q^4/(4 r_h^8)\bigr)$, 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 $η/s = (1/(4π))\bigl(1 + q_2\, 7κ^2 Q^4/(2 r_h^8)\bigr)$, 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 $1/(4π)$. 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.