Five-dimensional null & time-like supersymmetric geometries

TL;DR

This paper constructs five-dimensional supersymmetric solutions in supergravity where the Killing vector's norm is non-analytic at certain points, including explicit finite-charge examples asymptotic to AdS3×S2.

Contribution

It introduces new supersymmetric geometries with non-analytic Killing vector norms, expanding the known solution space in five-dimensional supergravity.

Findings

Existence of solutions with non-analytic Killing vector norms.

Explicit multi-center Gibbons-Hawking base constructions.

Finite-charge solutions asymptotic to AdS3×S2.

Abstract

We show that there exist supersymmetric solutions of five-dimensional, pure, $\mathcal{N}=1$ Supergravity such that the norm of the supersymmetric Killing vector, built out of the Killing spinor, is a real not-everywhere analytic function such that all its derivatives vanish at a point where the Killing vector field becomes null. The norm of the Killing vector field then is not an analytic function on a neighborhood around this point. We explicitly construct such solutions by using a multi-center Gibbons-Hawking base. Although many of these solutions have infinite charges, we find explicit examples with finite charges that asymptote to $AdS_3\times S_2$ and discuss their physical interpretation.