Equivariant bundle gerbes

TL;DR

This paper develops the theory of equivariant bundle gerbes, focusing on their characteristic classes, descent problems, and examples like the basic bundle gerbe on unitary groups and string structures, with applications to orbifold sigma models.

Contribution

It introduces the concept of simplicial extensions for bundle gerbes and analyzes their equivariance properties and characteristic classes, providing new insights into their structure and applications.

Findings

The basic bundle gerbe on a unitary group is equivariant under conjugation.

The characteristic class of the basic bundle gerbe is explicitly calculated.

A string structure induces an equivariant bundle gerbe for the String 2-group action.

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.