Spinorial Geometry and Supergravity

TL;DR

This thesis develops a spinorial geometry formalism for solving Killing spinor equations in supergravity, providing new solutions and insights into spacetime geometry, with applications to D=11 supergravity and heterotic string backgrounds.

Contribution

It introduces a comprehensive spinorial geometry method applicable to supergravity theories, including detailed solutions and analysis for D=11 supergravity and heterotic string backgrounds.

Findings

Many solutions to D=11 Killing spinor equations are presented.

The formalism links mathematical spin representations with supergravity solutions.

Alpha-prime corrections are incorporated to maintain anomaly cancellation.

Abstract

In the main part of this thesis, we present the foundations and initial results of the Spinorial Geometry formalism for solving Killing spinor equations. This method can be used for any supergravity theory, although we largely focus on D=11 supergravity. The D=5 case is investigated in an appendix. The exposition provides a comprehensive introduction to the formalism, and contains background material on the complex spin representations which, it is hoped, will provide a useful bridge between the mathematical literature and our methods. Many solutions to the D=11 Killing spinor equations are presented, and the consequences for the spacetime geometry are explored in each case. Also in this thesis, we consider another class of supergravity solutions, namely heterotic string backgrounds with (2,0) world-sheet supersymmetry. We investigate the consequences of taking alpha-prime corrections into account in the field equations, in order to remain consistent with anomaly cancellation, while requiring that spacetime supersymmetry is preserved.