Holographic charged transport with higher derivatives

A bstract We compute the first-order hydrodynamic transport coefficients (shear viscosity η , bulk viscosity ζ , and charge conductivity σ ) 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 (albeit without higher-derivative scalar gradient couplings), allowing for a systematic exploration of charged transport along generic holographic RG flows. The leading-order higher-derivative corrections probe gauge theories with unequal central charges c ≠ 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: the transport coefficients are extracted from black brane horizon data, including the horizon values of the bulk scalars and of the functions defining the gravitational dual. For the bulk viscosity and the conductivity, this horizon data also includes the corresponding zero-frequency diffeomorphism-invariant scalar and gauge-field fluctuations.