Symmetries of Gerbes and Applications in Geometry and Physics

Gerbes are geometric objects describing the third integer cohomology of a manifold and the B-field in string theory. They are related to line bundles in many ways, but their structure is significantly richer. Infinitesimal symmetries of gerbes on a manifold M are associated with algebroid structures on M. In this talk, we investigate finite symmetries of gerbes; we demonstrate how, in the presence of a Lie group action on M, gerbes on M lead to higher extensions of the acting Lie group. These extensions have several applications in geometry and physics: they explain non-associative magnetic translations, describe anomalies in QFTs in odd dimensions, and give rise to new models for the string group.