Gauduchon-Tod structures, Sim holonomy and De Sitter supergravity

TL;DR

This paper classifies null solutions in five-dimensional De Sitter supergravity using spinorial geometry, revealing their connection to Gauduchon-Tod structures, Kundt geometries, and Sim(3) holonomy, with explicit examples provided.

Contribution

It introduces a detailed classification of null solutions in De Sitter supergravity based on Gauduchon-Tod structures and their holonomy properties, extending understanding of supergravity geometries.

Findings

Null solutions are characterized by Gauduchon-Tod structures.

When these structures reduce to the 3-sphere, the null vector becomes recurrent.

All curvature invariants are constant in these geometries.

Abstract

Solutions of five-dimensional De Sitter supergravity admitting Killing spinors are considered, using spinorial geometry techniques. It is shown that the "null" solutions are defined in terms of a one parameter family of 3-dimensional constrained Einstein-Weyl spaces called Gauduchon-Tod structures. They admit a geodesic, expansion-free, twist-free and shear-free null vector field and therefore are a particular type of Kundt geometry. When the Gauduchon-Tod structure reduces to the 3-sphere, the null vector becomes recurrent, and therefore the holonomy is contained in Sim(3), the maximal proper subgroup of the Lorentz group SO(4,1). For these geometries, all scalar invariants built from the curvature are constant. Explicit examples are discussed.