Smooth 2-Group Extensions and Symmetries of Bundle Gerbes

Severin Bunk, Lukas Müller, Richard J. Szabo

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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
JournalCommunications in Mathematical Physics
Volume384
Issue number2
DOIs
Publication statusPublished - 28 Apr 2020

Keywords

  • math.DG
  • hep-th
  • math-ph
  • math.AT
  • math.MP

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