Thermodynamics of 4D dilatonic black holes and the weak gravity conjecture

Abstract

Taking a thermodynamic perspective, we study the weak gravity conjecture in the context of fourdimensional Einstein-Maxwell-dilaton theory. We find closed-form expressions for the corrected thermodynamic quantities in the presence of four-derivative terms in the action, and in particular the charge-to-mass ratio and entropy, for several families of solutions of special magnetic-to-electric charge ratio or dilaton coupling constant. Assuming that dyonic black holes themselves are the conjectured charged states, this places constraints on the Wilson coefficients of the theory which we show are satisfied for several generic UV completions.

A new spin on the Weak Gravity Conjecture

“…In this section, we will rewrite the shift to the extremality bound as a condition on the stress tensor that captures these corrections. In [10,11], it was explained in great detail (see also [26]) that corrections to the extremality bound in a canonical ensemble and corrections to the entropy in a microcanonical ensemble (fixed mass and charge) of an extremal black hole are directly related. At least for stationary black holes both corrections are determined by a modification of the same metric function f (r), whose roots give the location of the horizon of a black hole.…”

“…In fact, several proofs applying in different restricted settings and making use of thermodynamics [9,10] or unitarity and causality [10][11][12] have been given by now, but it has become clear that generically one needs additional UV information and that the WGC cannot follow solely from IR consistency. In the presence of a massless graviton, positivity bounds cannot completely constrain the correction to the extremality bound due to a singularity in the forward limit of graviton exchange in the t-channel (see [10][11][12][13][14] for recent discussions). 2 It is thus of interest to identify the minimal set of assumptions needed to prove the WGC.…”

Electromagnetic quasitopological gravities

“…This would allow for the decay of extremal black holes in terms of energy and charge conservation. Previous literature had studied perturbative corrections to the extremality bound in a variety of theories, ranging from general EFTs to Stringy effective actions [77][78][79][80][81][82][83][84][85][86]. Although our theories do not belong (a priori) to those categories, they have the advantage of allowing us to perform exact, non-perturbative computations.…”

“…On the other hand, the study of charged black holes with higher-derivative corrections is a current matter of research in the context of string phenomenology due to its relation with the Weak Gravity Conjecture (WGC) [76] -see e.g. [77][78][79][80][81][82][83][84][85][86]. In this respect, it may be interesting to analyze the effect of vector-curvature couplings on charged black holes, since those couplings indeed appear in stringy effective actions [87][88][89][90].…”

“…Perturbative higher-derivative corrections to the extremal charge-to-mass ratio have been recently explored in a number of papers, e.g. [77][78][79][80][81][82][83][84][85][86]. Our study, on the other hand, is fully non-perturbative, and we can analyze what happens when the corrections become important.…”