Characterization of all the supersymmetric solutions of gauged N=1,d=5 supergravity

TL;DR

This paper provides a comprehensive characterization of all supersymmetric solutions in gauged N=1, d=5 supergravity with matter fields, detailing metric forms and associated equations, highlighting the complexity of systematically constructing solutions.

Contribution

It offers the first complete description of all supersymmetric solutions in gauged N=1, d=5 supergravity with matter, including explicit metric forms and governing equations.

Findings

Derived generic metric forms as functions of scalars and vector fields

Formulated the complex non-linear system of equations for solutions

Highlighted the difficulty in systematically constructing all solutions

Abstract

We find a complete characterization of all the supersymmetric solutions of non-Abelian gauged N=1,d=5 supergravity coupled to vector multiplets and hypermultiplets: the generic forms of the metrics as functions of the scalars and vector fields plus the equations that all these must satisfy. These equations are now a complicated non-linear system and there it seems impossible to produce an algorithm to construct systematically all supersymmetric solutions.