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# Advances in Theoretical and Mathematical Physics

## Volume 21 (2017)

### Number 4

### Equivariant bundle gerbes

Pages: 921 – 975

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

#### Authors

#### 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

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