All timelike supersymmetric solutions of N=2, D=4 gauged supergravity coupled to abelian vector multiplets

TL;DR

This paper classifies all timelike supersymmetric solutions in N=2, D=4 gauged supergravity with abelian vector multiplets, revealing their geometric structure and potential for constructing new supersymmetric AdS black holes.

Contribution

It provides a complete classification of solutions using spinorial geometry, including the holonomy groups and geometric features, and discusses applications to black hole construction.

Findings

Holonomy group characterized as GL((8-N)/2,C) ⋉ N/2 C^((8-N)/2).

Spacetime is a fibration over a 3D base with U(1) holonomy.

Framework for constructing new supersymmetric AdS black holes.

Abstract

The timelike supersymmetric solutions of N=2, D=4 gauged supergravity coupled to an arbitrary number of abelian vector multiplets are classified using spinorial geometry techniques. We show that the generalized holonomy group for vacua preserving N supersymmetries is GL((8-N)/2,C) $\ltimes$ N/2 C^((8-N)/2) $\subseteq$ GL(8,R), where N=0,2,4,6,8. The spacetime turns out to be a fibration over a three-dimensional base manifold with U(1) holonomy and nontrivial torsion. Our results can be used to construct new supersymmetric AdS black holes with nontrivial scalar fields turned on.