Gerbes in classical Chern-Simons theory

TL;DR

This paper constructs a geometric gerbe associated with connections on principal SU(2)-bundles over closed 1-manifolds, exploring their properties and relations to connections over bounding 2-manifolds.

Contribution

It introduces a geometric construction of gerbes linked to SU(2)-bundle connections and analyzes their fundamental properties, including gluing laws.

Findings

Gerbes are assigned to connections on principal SU(2)-bundles over 1-manifolds.

A natural object in the gerbe arises from restrictions of connections over bounding 2-manifolds.

Gerbes and objects satisfy fundamental properties like gluing laws.

Abstract

We construct geometrically a gerbe assigned to a connection on a principal SU(2)-bundle over an oriented closed 1-dimensional manifold. If the connection is given by the restriction of a connection on a bundle over a compact 2-manifold bounding the 1-manifold, then we have a natural object in the gerbe. The gerbes and the objects satisfy certain fundamental properties, e.g. gluing law.