Abstract
We investigate higher-derivative extensions of Einstein-Maxwell theory that are invariant under electromagnetic duality rotations, allowing for non-minimal couplings between gravity and the gauge field. Working in a derivative expansion of the action, we characterize the Lagrangians giving rise to duality-invariant theories up to the eight-derivative level, providing the complete list of operators that one needs to include in the action. We also characterize the set of duality-invariant theories whose action is quadratic in the Maxwell field strength but which are non-minimally coupled to the curvature. Then we explore the effect of field redefinitions and we show that, to six derivatives, the most general duality-preserving theory can be mapped to Maxwell theory minimally coupled to a higher-derivative gravity containing only four non-topological higher-order operators. We conjecture that this is a general phenomenon at all orders, i.e., that any duality-invariant extension of Einstein-Maxwell theory is perturbatively equivalent to a higher-derivative gravity minimally coupled to Maxwell theory. Finally, we study charged black hole solutions in the six-derivative theory and we investigate additional constraints on the couplings motivated by the weak gravity conjecture.
Highlights
In this paper, we intend to study a more basic type of duality which already appears at the level of classical electrodynamics: electromagnetic duality
To the six-derivative level, all the higher-order terms involving Maxwell field strengths can be removed via field redefinitions
We have studied higher-order extensions of Einstein-Maxwell theory which are invariant under electromagnetic duality rotations
Summary
We determine the necessary and sufficient conditions for a higher-derivative theory to be invariant under duality rotations. Let us first start by noticing that, if the Lagrangian L depends non-degenerately on the derivatives of Fμν, the relation H(F ) given by (2.8) is differential. This means that the inverse relation F (H) must involve integration. If the equations of motion are invariant under duality rotations, this relation should be equivalent to the one obtained by inverting (2.8), but we see that this is not possible since, as we mentioned, F (H) must involve integration while (2.15) is again differential. The conclusion is that the equations of motion cannot be duality invariant if the Lagrangian contains derivatives of the field strength. Let us study which further constraints duality invariance imposes on the Lagrangian
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