Holographic transport beyond the supergravity approximation

We set up a unified framework to efficiently compute the shear and bulk viscosities of strongly coupled gauge theories with gravitational holographic duals involving higher derivative corrections. We consider both Weyl$^4$ corrections, encoding the finite 't Hooft coupling corrections of the boundary theory, and Riemann$^2$ corrections, responsible for non-equal central charges $c\ne a$ of the theory at the ultraviolet fixed point. Our expressions for the viscosities in higher derivative holographic models are extracted from a radially conserved current and depend only on the horizon data.