Supersymmetry and Lorentzian holonomy in various dimensions

TL;DR

This paper introduces a systematic method for constructing Lorentzian manifolds with special holonomy that serve as non-static supersymmetric vacua, extending Riemannian techniques and allowing moduli to vary with light-cone time.

Contribution

It develops a novel formalism for generating non-static supersymmetric solutions with Lorentzian holonomy, including explicit examples across multiple dimensions.

Findings

Constructed new classes of non-static supersymmetric vacua.

Demonstrated how to promote moduli to functions of light-cone time.

Provided detailed examples in various dimensions.

Abstract

We present a systematic method for constructing manifolds with Lorentzian holonomy group that are non-static supersymmetric vacua admitting covariantly constant light-like spinors. It is based on the metric of their Riemannian counterparts and the realization that, when certain conditions are satisfied, it is possible to promote constant moduli parameters into arbitrary functions of the light-cone time. Besides the general formalism, we present in detail several examples in various dimensions.