Action Growth of Dyonic Black Holes and Electromagnetic Duality
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.
Keywords
Cite
@article{arxiv.1905.06409,
title = {Action Growth of Dyonic Black Holes and Electromagnetic Duality},
author = {Hai-Shan Liu and H. Lu},
journal= {arXiv preprint arXiv:1905.06409},
year = {2019}
}
Comments
Latex, 26 pages, references added