Hydrodynamics of nonminimal <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mi>F</mml:mi> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>a</mml:mi> <mml:mo>)</mml:mo> <mml:mi>α</mml:mi> <mml:mi>β</mml:mi> </mml:mrow> </mml:msup> <mml:msup>

Abstract We investigate the hydrodynamic properties of a strongly coupled non-Abelian plasma dual to a four-dimensional anti-de Sitter black brane with a nonminimal coupling of the form q 2 F ( a ) α β F ( a ) γ λ R α γ R β λ 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 ⩾ 1 in units where ℏ = 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 ( 9 κ Q 2 / ( L 2 r h 4 ) + 7 κ 2 Q 4 / ( 4 r 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 η / s = ( 1 / ( 4 π ) ) ( 1 + q 2 7 κ 2 Q 4 / ( 2 r h 8 ) ) , showing that the Kovtun–Son–Starinets 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 π ) . 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.