Hydrodynamical transports in generic AdS Gauss-Bonnet-scalar Gravity

Abstract: The experimentally observed temperature-dependent shear and bulk viscosities of the quark-gluon plasma (QGP), along with its apparent violation of the Kovtun-Son-Starinets (KSS) bound $\eta/s=1/(4\pi)$, necessitate a holographic description that incorporates higher-derivative corrections. We propose a five-dimensional Einstein-Scalar-Maxwell-Gauss-Bonnet model in which a scalar-Gauss-Bonnet coupling $H(\phi)$ encodes leading curvature corrections. Although no closed-form black hole solution is available, we employ an entropy-production analysis at the event horizon to derive exact analytic formulas for the shear viscosity $\eta$ and bulk viscosity $\zeta$. These expressions exhibit apparent deviation from the KSS bound and nontrivial temperature dependence. We then perform an independent computation via the retarded Green function (Kubo) method, finding perfect agreement for $\eta$ and isolating a single constant in $\zeta$ that requires numerical determination. Our dual derivation underscores the pivotal role of higher-derivative terms in realistic QGP modeling and demonstrates the efficacy of nonanalytic holographic backgrounds in capturing the dynamics of strongly coupled fluids.