Supersymmetry, holonomy and Kundt spacetimes

TL;DR

This paper explores the relationship between supersymmetry, special holonomy, and Kundt spacetimes in supergravity, revealing their unique properties and potential implications for fundamental physics.

Contribution

It characterizes Lorentzian manifolds with special holonomy, identifying conditions under which they belong to the Kundt class and discussing their physical significance.

Findings

Lorentzian manifolds are either reducible or have degenerate holonomy invariant lightlike subspaces.

Kundt spacetimes include special cases like vanishing and constant curvature spacetimes.

These spacetimes have unique properties that could impact fundamental physics.

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.