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

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.