Holographic Charged Transport with Higher Derivatives

Abstract

We compute the first-order hydrodynamic transport coefficients (shear viscosity $\eta$, bulk viscosity $\zeta$, and charge conductivity $\sigma$) for a broad class of strongly coupled, four-dimensional charged relativistic gauge theory plasma with holographic gravitational duals containing higher-derivative corrections. The landscape of our holographic models captures non-conformal gauge theories with an arbitrary number of relevant coupling constants and a general scalar potential in the gravitational dual, allowing for a systematic exploration of charged transport along generic holographic RG flows. The leading-order higher-derivative corrections probe gauge theories with non-equal central charges $c\ne a$ at the ultraviolet fixed point, and enable the engineering of diverse temperature and charge density profiles for the viscosities and the conductivity. Our results establish the membrane paradigm in higher-derivative holographic models: all the transport coefficients are extracted from the black brane horizon values of the gravitational scalars, and various functions defining the gravitational holographic dual.