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

References in corpus (4)

• Classification of the Weyl Tensor in Higher Dimensions and Applications
• Holonomy and Symmetry in M-theory
• Metrics With Vanishing Quantum Corrections
• Lorentzian spacetimes with constant curvature invariants in three dimensions

Cited by in corpus (1)

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