nLab
Chern-Simons gerbe

Idea

A Chern-Simons gerbe is a lifting gerbe for the shifted central extension

$$BU(1)\to \mathrm{String}(G)\to G$$\mathbf{B}U(1) \to String(G) \to G

given by the string group.

This is called “Chern-Simons gerbe” because for a given $G$-principal bundle $P$; the corresponding Chern-Simons gerbe has the property that

• the integral class of the gerbe is the first (fractional) Pontryagin class of $P$

• a connection on the Chern-Simons gerbe has as curvature 3-form the Chern-Simons form of a connection on $P$.