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

TL;DR

This paper develops holographic renormalization for Einstein-Maxwell theory with curvature-squared corrections, analyzing black hole thermodynamics and the mass-charge relation, and exploring implications for the weak gravity conjecture and dual CFT constraints.

Contribution

It constructs boundary counterterms for higher-derivative gravity, ensuring a well-defined variational principle and ghost-free perturbations, and studies their effects on black hole properties.

Findings

Higher derivative couplings influence the mass-charge ratio of extremal black holes.

Sign of higher derivative terms relates to the weak gravity conjecture.

Connections between higher derivatives, viscosity bounds, and CFT central charges.

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.