We carry out the holographic renormalization of Einstein-Maxwell theory with
curvature-squared corrections. In particular, we demonstrate how to construct
the generalized Gibbons-Hawking surface term needed to ensure a perturbatively
well-defined variational principle. This treatment ensures the absence of ghost
degrees of freedom at the linearized perturbative order in the
higher-derivative corrections. We use the holographically renormalized action
to study the thermodynamics of R-charged black holes with higher derivatives
and to investigate their mass to charge ratio in the extremal limit. In five
dimensions, there seems to be a connection between the sign of the higher
derivative couplings required to satisfy the weak gravity conjecture and that
violating the shear viscosity to entropy bound. This is in turn related to
possible constraints on the central charges of the dual CFT, in particular to
the sign of c-a.Comment: 30 pages. v2: references added, some equations simplifie
