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J. High Energ. Phys. 1909 (2019) 102.          arXiv link

Action growth of dyonic black holes and electromagnetic duality

Hai-Shan Liu1,2, H. Lü1,*

1. Center for Joint Quantum Studies and Department of Physics, School of Science, Tianjin University, Tianjin, China

2. Institute for Advanced Physics & Mathematics, Zhejiang University of Technology, Hangzhou, China

* mrhonglu@gmail.com 

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 lose this duality. It was recently proposed in arXivid: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 is preserved 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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