Action Growth of Dyonic Black Holes and Electromagnetic Duality

Understand

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.