Higher Derivative Corrections to R-charged Black Holes: Boundary Counterterms and the Mass-Charge Relation

TL;DR

This work formulates a perturbative holographic renormalization framework for Einstein–Maxwell theory with curvature–squared corrections, introducing a generalized Gibbons–Hawking term and boundary counterterms to ensure a well-posed variational principle and finite on-shell action. It then derives the linear-order r^2-corrected, R-charged AdS black hole solutions, computes their thermodynamics, and examines how the mass–charge relation is altered in the extremal limit. A central result is that the sign and magnitude of the higher-derivative couplings influence m/q and transport coefficients, revealing a link between the weak gravity conjecture and holographic bounds such as η/s, with implications for the dual CFT central charges. The study emphasizes the need for UV-derived constraints on the couplings to maintain consistency with quantum gravity and AdS/CFT duality.

Abstract

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.