Supersymmetry, holonomy and Kundt spacetimes

2008/07/31 by Johan Brännlund, J Brannlund, A. A. Coley +3 · 1 citation
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Noncommutative and Quantum Gravity Theories #gr-qc #hep-th

paper · pdf · doi:10.1088/0264-9381/25/19/195007

published as Class.Quant.Grav.25:195007,2008 · 14 pages. Accepted by Class. Quant. Grav. Some misprints fixed

arxiv created 2008/07/31 · openalex publication_date 2008/09/11 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Classification of the Weyl tensor in higher dimensions and applications
• A class of exact pp-wave string models with interacting light-cone gauge actions
• A Class of Exact Classical Solutions to String Theory
• Strings on pp-waves and massive two dimensional field theories
• Spacetime singularities in string theory
• Einstein Manifolds

Cited by

• One component of the curvature tensor of a Lorentzian manifold