Exact electromagnetic duality with nonminimal couplings

TL;DR

This paper develops a class of Einstein-Maxwell theories with exact electromagnetic duality, deriving a closed-form action with quadratic vector field dependence, and analyzes black hole solutions, revealing novel charge and entropy properties.

Contribution

It introduces a closed-form action for duality-invariant nonminimal Einstein-Maxwell theories with quadratic dependence on the vector field, and studies their black hole solutions.

Findings

Derived a closed-form action with higher-derivative terms.

Found black hole solutions invariant under electric-magnetic charge rotations.

Discovered constant entropy correction and bounds on extremal black hole charge and mass.

Abstract

We study nonminimal extensions of Einstein-Maxwell theory with exact electromagnetic duality invariance. Any such theory involves an infinite tower of higher-derivative terms whose computation and summation usually represents a challenging problem. Despite that, we manage to obtain a closed form of the action for all the theories with a quadratic dependence on the vector field strength. In these theories we find that the Maxwell field couples to gravity through a curvature-dependent susceptibility tensor that takes a peculiar form, reminiscent of that of Born-Infeld Lagrangians. We study the static and spherically symmetric black hole solutions of the simplest of these models, showing that the corresponding equations of motion are invariant under rotations of the electric and magnetic charges. We compute the perturbative corrections to the Reissner-Nordstr\"om solution in this theory, and in the case of extremal black holes we determine exactly the near-horizon geometry as well as the entropy. Remarkably, the entropy only possesses a constant correction despite the action containing an infinite number of terms. In addition, we find there is a lower bound for the charge and the mass of extremal black holes. When the sign of the coupling is such that the weak gravity conjecture is satisfied, the area and the entropy of extremal black holes vanish at the minimal charge.