0804.4835Apr 30, 200850 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

Multiplicative Bundle Gerbes with Connection

Konrad Waldorf

Differential Geometry

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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.

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