Supersymmetric solutions of N=2 d=4 sugra: the whole ungauged shebang

TL;DR

This paper completes the classification of supersymmetric solutions in N=2 D=4 ungauged supergravity with vector and hypermultiplets, revealing how hypermultiplets influence the geometry and solution structure.

Contribution

It extends previous classifications by including hypermultiplets, showing their effect on the geometry and harmonic functions in supersymmetric solutions.

Findings

Hypermultiplets cause the hypersurfaces to be curved with SU(2) holonomy.

Solutions depend on harmonic functions in curved 3D space.

Null solutions restrict hyperscalars to null coordinate dependence.

Abstract

In this article we complete the classification of the supersymmetric solutions of N=2 D=4 ungauged supergravity coupled to an arbitrary number of vector- and hypermultiplets. We find that in the timelike case the hypermultiplets cause the constant-time hypersurfaces to be curved and have su(2) holonomy identical to that of the hyperscalar manifold. The solutions have the same structure as without hypermultiplets but now depend on functions which are harmonic in the curved 3-dimensional space. We discuss an example obtained from a hyper-less solution via the c-map. In the null case we find that the hyperscalars can only depend on the null coordinate and the solutions are essentially those of the hyper-less case.