Smooth 2-Group Extensions and Symmetries of Bundle Gerbes

Understand

We study bundle gerbes on manifolds $M$ that carry an action of a connected Lie group $G$.

• We show that these data give rise to a smooth 2-group extension of $G$ by the smooth 2-group of hermitean line bundles on $M$.
• This 2-group extension classifies equivariant structures on the bundle gerbe, and its non-triviality poses an obstruction to the existence of equivariant structures.
• We present a new global approach to the parallel transport of a bundle gerbe with connection, and use it to give an alternative construction of this smooth 2-group extension in terms of a homotopy-coherent version of the associated bundle construction.