Supersymmetry of topological Kerr-Newmann-Taub-NUT-aDS spacetimes

TL;DR

This work analyzes topological Kerr-Newman-Taub-NUT-AdS spacetimes within gauged N=2, d=4 supergravity, introducing NUT charge and cosmological-constant-driven generalizations (RN-TN-$aDS$, KN-TN-$aDS$, RB-$aDS$) and showing all arise as limits of the Plebanski-Demianski solution. By computing the Killing spinor integrability conditions, the authors determine supersymmetry fractions, finding that generic rotating configurations preserve at most 1/4 of the supersymmetry, with non-rotating cases able to reach 1/2 SUSY in special limits; the Plebanski-Demianski family reveals a continuous SO(2) electric-magnetic duality that rotates mass and NUT charge with electric and magnetic charges, although gauging breaks the naive duality. The key contribution is the explicit linking of a broad class of topological AdS spacetimes to precise SUSY bounds and duality relations, clarifying when and how supersymmetry can be preserved in complex charged, rotating backgrounds. This has potential implications for the structure of supersymmetric solutions in AdS/CFT contexts and for understanding central charges and dualities in gauged supergravity.

Abstract

We extend the topological Kerr-Newman-aDS solutions by including NUT charge and find generalizations of the Robinson-Bertotti solution to the negative cosmological constant case with different topologies. We show how all these solutions can be obtained as limits of the general Plebanski-Demianski solution. We study the supersymmetry properties of all these solutions in the context of gauged N=2,d=4 supergravity. Generically they preserve at most 1/4 of the total supersymmetry. In the Plebanski-Demianski case, although gauged N=2,d=4 supergravity does not have electric-magnetic duality, we find that the family of supersymmetric solutions still enjoys a sort of electric-magnetic duality in which electric and magnetic charges and mass and Taub-NUT charge are rotated simultaneously.