Supersymmetry, holonomy and Kundt spacetimes

Abstract

Supersymmetric solutions of supergravity theories, and consequently metrics with special holonomy, have played an important role in the development of string theory. We describe how a Lorentzian manifold is either completely reducible, and thus essentially known, or not completely reducible so that there exists a degenerate holonomy invariant lightlike subspace and consequently admits a covariantly constant or a recurrent null vector and belongs to the higher-dimensional Kundt class of spacetimes. These Kundt spacetimes (which contain the vanishing and constant curvature invariant spacetimes as special cases) are genuinely Lorentzian and have a number of interesting and unusual properties, which may lead to novel and fundamental physics.

14 pages. Accepted by Class. Quant. Grav. Some misprints fixed

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Cited by in corpus (19)

• Kundt Spacetimes
• General Kundt spacetimes in higher dimensions
• Gauduchon-Tod structures, Sim holonomy and De Sitter supergravity
• On the local structure of Lorentzian Einstein manifolds with parallel distribution of null lines
• Hidden symmetries of Eisenhart-Duval lift metrics and the Dirac equation with flux
• A spacetime not characterised by its invariants is of aligned type II
• Lorentzian manifolds and scalar curvature invariants
• One component of the curvature tensor of a Lorentzian manifold
• Generalized Teleparallel de Sitter geometries
• Kundt Three Dimensional Left Invariant Spacetimes
• Holonomy of Einstein Lorentzian manifolds
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• Examples of Einstein spacetimes with recurrent null vector fields
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• Vacuum Einstein field equations in smooth metric measure spaces: the isotropic case
• Killing Spinors -- Beyond Supergravity