Solitonic sectors, conformal boundary conditions and three-dimensional topological field theory
arXiv:hep-th/0009111
Abstract
The correlation functions of a two-dimensional rational conformal field theory, for an arbitrary number of bulk and boundary fields and arbitrary world sheets can be expressed in terms of Wilson graphs in appropriate three-manifolds. We present a systematic approach to boundary conditions that break bulk symmetries. It is based on the construction, by `alpha-induction', of a fusion ring for the boundary fields. Its structure constants are the annulus coefficients and its 6j-symbols give the OPE of boundary fields. Symmetry breaking boundary conditions correspond to solitonic sectors.
9 pages, LaTeX2e. Invited talk by Christoph Schweigert at the TMR conference ``Non-perturbative quantum effects 2000'', Paris, September 2000