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

TL;DR

The paper resolves an apparent clash between BPS bounds in four-dimensional $N=2$ gauged supergravity and Romans' supersymmetric solutions by showing two distinct BPS ground states, each tied to a different asymptotic geometry (AdS$_4$ and magnetic AdS$_4$). Using Noether currents and explicit Killing spinor analysis, the authors derive two independent superalgebras and corresponding BPS bounds: for AdS$_4$ with no magnetic charge, $M \ge |Q_e| + g|\vec{J}|$ (reducing to $M \ge |Q_e|$ in the static case); for magnetic AdS$_4$ with $Q_m = \pm 1/(2g)$, $M \ge 0$ with $Q_e$ and $\vec{J}$ unconstrained. They provide a built-in holographic renormalization within the SUSY algebra that yields finite conserved charges for AdS$_4$ backgrounds, and clarify how the cosmic monopole solutions saturate the magnetic AdS$_4$ bound. The results reconcile the Rämous BPS structure with the full gauged supergravity framework and offer insights for AdS/CFT in magnetic backgrounds.

Abstract

We determine the BPS bounds in minimal gauged supergravity in four spacetime 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 superalgebra 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.