Gauduchon-Tod structures, Sim holonomy and De Sitter supergravity

Details Gauduchon-Tod structures, Sim holonomy and De Sitter supergravity Gauduchon-Tod structures, Sim holonomy and De Sitter supergravity

2009-05-19

arxiv.org/abs/0905.3047v2

JHEP 0907:069,2009

Physics

High Energy Physics

High Energy Physics - Theory

1+21 pages, no figures; v2 minor changes, typos corrected, matches published version in JHEP

Scientific paper

10.1088/1126-6708/2009/07/069

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.

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