Multiplicative Bundle Gerbes with Connection

TL;DR

This paper introduces connections on multiplicative bundle gerbes over Lie groups and demonstrates their role in constructing central extensions, Chern-Simons actions, and bi-branes in WZW models.

Contribution

It provides a systematic study of connections on multiplicative bundle gerbes and links them to important geometric and physical structures.

Findings

Constructs smooth central extensions of loop groups

Develops Chern-Simons actions for various gauge groups

Describes symmetric bi-branes for WZW models

Abstract

Multiplicative bundle gerbes are gerbes over a Lie group which are compatible with the group structure. In this article connections on such bundle gerbes are introduced and studied. It is shown that multiplicative bundle gerbes with connection furnish geometrical constructions of the following objects: smooth central extensions of loop groups, Chern-Simons actions for arbitrary gauge groups, and symmetric bi-branes for WZW models with topological defect lines.