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arXiv · 1905.06409

Action Growth of Dyonic Black Holes and Electromagnetic Duality

Hai-Shan Liu·H. Lu
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Abstract

Electromagnetic duality of Maxwell theory is a symmetry of equations but not of the action. The usual application of the `complexity=action' conjecture would thus loose this duality. It was recently proposed in arxiv:1901.00014 that the duality can be restored by adding some appropriate boundary term, at the price of introducing the mixed boundary condition in the variation principle. We present universal such a term in both first-order and second-order formalism for a general theory of a minimally-coupled Maxwell field. The first-order formalism has the advantage that the variation principle involves only the Dirichlet boundary condition. Including this term, we compute the on-shell actions in the Wheeler-De Witt patch and find that the duality persists in these actions for a variety of theories, including Einstein-Maxwell, Einstein-Maxwell-Dilaton, Einstein-Born-Infeld and Einstein-Horndeski-Maxwell theories.

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Hai-Shan Liu, H. Lu. 2019-05-28. Action Growth of Dyonic Black Holes and Electromagnetic Duality. https://doi.org/10.1007/jhep09(2019)102

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