All the timelike supersymmetric solutions of all ungauged d=4 supergravities

TL;DR

This paper classifies all timelike supersymmetric solutions in ungauged d=4 supergravities with N≥2, revealing they relate to N=2 truncations and depend on harmonic functions, with solutions' properties linked to scalar field configurations.

Contribution

It provides a complete characterization of all such solutions using a symmetry-preserving approach and spinor-bilinears, extending previous conjectures about their structure.

Findings

Solutions are associated with N=2 truncations including hypermultiplets.

The solutions depend on harmonic functions related to the number of vector fields.

The transverse space's flatness depends on the triviality of hyperscalars.

Abstract

We determine the form of all timelike supersymmetric solutions of all N greater or equal than 2, d=4 ungauged supergravities, for N less or equal than 4 coupled to vector supermultiplets, using the $Usp(n+1,n+1)-symmetric formulation of Andrianopoli, D'Auria and Ferrara and the spinor-bilinears method, while preserving the global symmetries of the theories all the way. As previously conjectured in the literature, the supersymmetric solutions are always associated to a truncation to an N=2 theory that may include hypermultiplets, although fields which are eliminated in the truncations can have non-trivial values, as is required by the preservation of the global symmetry of the theories. The solutions are determined by a number of independent functions, harmonic in transverse space, which is twice the number of vector fields of the theory (n+1). The transverse space is flat if an only if the would-be hyperscalars of the associated N=2 truncation are trivial.