Einstein Weyl Structures and de Sitter Supergravity

TL;DR

This paper explores the geometric structures of null solutions in five-dimensional de Sitter supergravity, focusing on Kundt metrics and special base spaces, revealing new examples and detailed cases related to holonomy and near horizon geometries.

Contribution

It provides a detailed analysis of null solutions in de Sitter supergravity, including explicit examples and special cases with unique geometric and holonomy properties.

Findings

Identification of Kundt metrics from Gauduchon-Tod base spaces

Examples including near horizon geometries

Analysis of solutions with recurrent null 1-form Killing spinor bilinear

Abstract

The geometric structure of the null solutions of de Sitter D=5 gauged supergravity coupled to vector multiplets is investigated. These solutions are Kundt metrics, constructed from a one-parameter family of three dimensional Gauduchon-Tod base spaces. We give examples, including the near horizon geometries previously found in arxiv:hep-th/10122120. In addition, two special cases are considered in detail. In the first, we consider solutions for which the Gauduchon-Tod base space is the Berger sphere. In the second case we take the null 1-form Killing spinor bilinear to be recurrent, so that the holonomy of the Levi-Civita connection is contained in Sim(3).