Combinatorial gerbes and gauge theories

by Romain ATTAL (Jussieu)

Tuesday 21 May 2002, 14:00 → 15:00 Europe/Zurich

TH Auditorium (CERN)

Gerbes are fibered spaces where surfaces can be lifted naturally (the usual principal or vector bundles are, in a sense, too small to realise this operation). We will present a combinatorial construction of such spaces, which are fibered categories, and explain how the usual notions of connection and curvature can be generalized to this context, especially when the gauge group is non-abelian. The key principle is functoriality, which subsumes any gauge symmetry. As an application, we will show how gerbes provide the right setting for BF-type field theories.