Smooth 2-group extensions and symmetries of bundle gerbes

DOI10.1007/S00220-021-04099-7zbMATH Open1467.81086arXiv2004.13395OpenAlexW3022969285MaRDI QIDQ2031133

Author name not available (Why is that?)

Publication date: 8 June 2021

Published in: (Search for Journal in Brave)

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

.

Full work available at URL: https://arxiv.org/abs/2004.13395

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