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.Comment: 9 pages, LaTeX2e. Invited talk by Christoph Schweigert at the TMR
conference ``Non-perturbative quantum effects 2000'', Paris, September 200
