Torsion parallel spinors on Lorentzian four-manifolds and supersymmetric evolution flows on bundle gerbes

TL;DR

This paper explores the geometry of torsion parallel spinors on Lorentzian four-manifolds and their relation to supersymmetric evolution flows on bundle gerbes, linking supergravity, string theory, and gauge theory.

Contribution

It introduces a geometric framework connecting torsion parallel spinors with supersymmetric flows and bundle gerbes, advancing understanding in supergravity and string theory contexts.

Findings

Characterization of torsion parallel spinors on Lorentzian four-manifolds

Development of supersymmetric evolution flows on bundle gerbes

Gauge-theoretic interpretation of skew-torsion as gerbe curvature

Abstract

This dissertation is concerned with the geometric study of differential spinors on oriented and spin Lorentzian four-manifolds via the theory of spinorial polyforms. The main results and applications are directed towards the investigation of torsion parallel spinors and the globally hyperbolic evolution flow determined by the globally hyperbolic solutions of the four-dimensional supersymmetric NS-NS system. This differential system, which originates in supergravity and string theory, involves skew-torsion parallel spinors subject to a curvature condition and provides a natural gauge-theoretic interpretation of skew-symmetric torsion as the curvature of a connection on an abelian bundle gerbe - a natural categorification of the notion of principal circle bundle.