Conformal Killing spinors and special geometric structures in Lorentzian geometry - a survey

TL;DR

This survey explores special geometric structures in Lorentzian geometry that admit conformal Killing spinors, focusing on dimensions up to six and their relevance in string theory contexts.

Contribution

It provides a comprehensive overview of Lorentzian geometries with conformal Killing spinors, highlighting classifications and examples up to dimension six.

Findings

Identification of Lorentzian geometries admitting conformal Killing spinors

Classification results for dimensions up to six

Connections to structures in string theory

Abstract

This paper is a survey on special geometric structures that admit conformal Killing spinors based on lectures, given at the ``Workshop on Special Geometric Structures in String Theory'', Bonn, September 2001 and at ESI, Wien, November 2001. We discuss the case of Lorentzian signature and explain which geometries occur up to dimension 6.