Multiplicative Bundle Gerbes with Connection

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.

50 pages; v2: minor changes; v3: exposition improved, one convention in Definition 1.3 changed, accordant changes throughout the whole paper, many details added in Section 2, Section 3.1 is completely rewritten, all main results unchanged, v4: minor changes, final version. Differential Geom. Appl., to appear

References in corpus (4)

• Twisted K-theory and loop group representations
• Unoriented WZW Models and Holonomy of Bundle Gerbes
• Bi-branes: Target Space Geometry for World Sheet topological Defects
• Constructions with bundle gerbes

Cited by in corpus (1)

• A Construction of String 2-Group Models using a Transgression-Regression Technique