On BPS bounds in D = 4 N = 2 gauged supergravity

We determine the BPS bounds in minimal gauged supergravity in four space- time dimensions. We concentrate on asymptotically anti-de Sitter (AdS) spacetimes, and find that there exist two disconnected BPS ground states of the theory, depending on the presence of magnetic charge. Each of these ground states comes with a different superal-gebra and a different BPS bound, which we derive. As a byproduct, we also demonstrate how the supersymmetry algebra has a built-in holographic renormalization method to define finite conserved charges