Gerbes, (twisted) K-theory, and the supersymmetric WZW model

2002/06/17 by Jouko Mickelsson, Mickelsson, Jouko
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Noncommutative and Quantum Gravity Theories #hep-th #math.DG

paper · pdf · doi:10.48550/arxiv.hep-th/0206139

some typos corrected, a short comment in the end and two references added

openalex publication_date 2002/06/17 · arxiv created 2002/12/06 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The aim of this talk is to explain how symmetry breaking in a quantum field theory problem leads to a study of projective bundles, Dixmier-Douady classes, and associated gerbes. A gerbe manifests itself in different equivalent ways. Besides the cohomological description as a DD class, it can be defined in terms of a family of local line bundles or as a prolongation problem for an (infinite-dimensional) principal bundle, with the fiber consisting of (a subgroup of) projective unitaries in a Hilbert space. The prolongation aspect is directly related to the appearance of central extensions of (broken) symmetry groups. We also discuss the construction of twisted K-theory classes by families of supercharges for the supersymmetric Wess-Zumino-Witten model.

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