Smooth 2-Group Extensions and Symmetries of Bundle Gerbes

Severin Bunk, Lukas Müller, Richard J. Szabo

Research output: Contribution to journalArticlepeer-review

Abstract

We study bundle gerbes on manifolds M that carry an action of a connected Lie group G. We show that these data give rise to a smooth 2-group extension of G by the smooth 2-group of hermitean line bundles on M. This 2-group extension classifies equivariant structures on the bundle gerbe, and its non-triviality poses an obstruction to the existence of equivariant structures. We present a new global approach to the parallel transport of a bundle gerbe with connection, and use it to give an alternative construction of this smooth 2-group extension in terms of a homotopy-coherent version of the associated bundle construction. We apply our results to give new descriptions of nonassociative magnetic translations in quantum mechanics and the Faddeev–Mickelsson–Shatashvili anomaly in quantum field theory. We also propose a definition of smooth string 2-group models within our geometric framework. Starting from a basic gerbe on a compact simply-connected Lie group G, we prove that the smooth 2-group extensions of G arising from our construction provide new models for the string group of G.

Original languageEnglish
Pages (from-to)1829-1911
Number of pages83
JournalCommunications in Mathematical Physics
Volume384
Issue number3
Early online date25 May 2021
DOIs
Publication statusPublished - Jun 2021

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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