Advances in Theoretical and Mathematical Physics

Volume 21 (2017)

Number 4

Equivariant bundle gerbes

Pages: 921 – 975

DOI: https://dx.doi.org/10.4310/ATMP.2017.v21.n4.a3

Authors

Michael K. Murray (School of Mathematical Sciences, University of Adelaide, SA, Australia)

David Michael Roberts (School of Mathematical Sciences, University of Adelaide, SA, Australia)

Danny Stevenson (School of Mathematical Sciences, University of Adelaide, SA, Australia)

Raymond F. Vozzo (School of Mathematical Sciences, University of Adelaide, SA, Australia)

Abstract

We develop the theory of simplicial extensions for bundle gerbes and their characteristic classes with a view towards studying descent problems and equivariance for bundle gerbes. Equivariant bundle gerbes are important in the study of orbifold sigma models. We consider in detail two examples: the basic bundle gerbe on a unitary group and a string structure for a principal bundle. We show that the basic bundle gerbe is equivariant for the conjugation action and calculate its characteristic class; we show also that a string structure gives rise to a bundle gerbe which is equivariant for a natural action of the String 2-group.

2010 Mathematics Subject Classification

18G30, 53C80, 55R91

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This research was supported under Australian Research Council’s Discovery Projects funding scheme (project numbers DP120100106 and DP130102578).

Published 10 October 2017