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

2025/07/08 by C. S. Shahbazi, Shahbazi, C. S. · 1 citation
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Geometric Analysis and Curvature Flows #High Energy Physics - Theory (hep-th) #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2507.06228

openalex publication_date 2025/07/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Cited by

• The Cauchy problem for gradient generalized Ricci solitons on a bundle gerbe

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