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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Liu, HS., Lü, H. Action growth of dyonic black holes and electromagnetic duality. J. High Energ. Phys. 2019, 102 (2019). https://doi.org/10.1007/JHEP09(2019)102
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DOI: https://doi.org/10.1007/JHEP09(2019)102