The supersymmetric configurations of N=2, d=4 supergravity coupled to vector supermultiplets

TL;DR

This work classifies all supersymmetric configurations of ungauged $N=2,d=4$ supergravity with vector multiplets by exploiting Killing spinor identities and bilinears to separate timelike and null sectors. In the timelike class, solutions reduce to Behrndt–Lüst–Sabra-type configurations determined by a real harmonic section $\mathcal{I}$ and stabilized by the stabilization equations, with the metric and vector fields explicitly constructed from symplectic data. The null class yields Brinkmann-type pp-waves with scalars depending on $u$ and holomorphic data; supersymmetry can be preserved by a half or all of the supercharges, including maximally supersymmetric Minkowski and Kowalski-Glikman-type waves. The results illuminate the role of special geometry, dualities, and harmonic/holomorphic data in shaping the full landscape of supersymmetric vacua and provide a foundation for extending the classification to more general theories.

Abstract

We classify all the supersymmetric configurations of ungauged N=2,d=4 supergravity coupled to n vector multiplets and determine under which conditions they are also classical solutions of the equations of motion. The supersymmetric configurations fall into two classes, depending on the timelike or null nature of the Killing vector constructed from Killing spinor bilinears. The timelike class configurations are essentially the ones found by Behrndt, Luest and Sabra, which exhaust this class and are the ones that include supersymmetric black holes. The null class configurations include pp-waves and cosmic strings.