Electric/magnetic duality of dyonic Kerr-Newman-NUT-AdS spacetimes

We study the (anti-)self-duality conditions under which the electric and magnetic parts of the conserved charges of the dyonic Kerr-Newman-NUT-AdS solution become equivalent. Within a holographic framework, the stress tensor and the boundary Cotton tensor are computed from the electric/magnetic content of the Weyl tensor. The holographic stress tensor/Cotton tensor duality is recovered along the (anti-)self-dual curve in parameter space. We show that the latter not only implies a duality relation for the mass but also for the angular momentum. The partition function is computed to first order in the saddle-point approximation and a BPS bound is obtained. The ground state of the theory is enlarged to all the (anti-)self-dual configurations when the $SO(4)$ and $U(1)$ Pontryagin densities are introduced. We demonstrate this at the level of the action and variations thereof.