Combinatorics of Non-Abelian Gerbes with Connection and Curvature

Details Combinatorics of Non-Abelian Gerbes with Connection and Curvature Combinatorics of Non-Abelian Gerbes with Connection and Curvature

2002-03-27

arxiv.org/abs/math-ph/0203056v1

Annales Fond.Broglie 29 (2004) 609-634

Physics

Mathematical Physics

20 pages ; uses AMS-LaTeX and XY-pic

Scientific paper

We give a functorial definition of $G$-gerbes over a simplicial complex when the local symmetry group $G$ is non-Abelian. These combinatorial gerbes are naturally endowed with a connective structure and a curving. This allows us to define a fibered category equipped with a functorial connection over the space of edge-paths. By computing the curvature of the latter on the faces of an infinitesimal 4-simplex, we recover the cocycle identities satisfied by the curvature of this gerbe. The link with $BF$-theories suggests that gerbes provide a framework adapted to the geometric formulation of strongly coupled gauge theories.

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