Advances in Theoretical and Mathematical Physics
Volume 21 (2017)
Equivariant bundle gerbes
Pages: 921 – 975
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).