Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2009-07-03
Nucl.Phys.B824:333-364,2010
Physics
High Energy Physics
High Energy Physics - Theory
Scientific paper
10.1016/j.nuclphysb.2009.07.017
It is known that reflection coefficients for bulk fields of a rational conformal field theory in the presence of an elementary boundary condition can be obtained as representation matrices of irreducible representations of the classifying algebra, a semisimple commutative associative complex algebra. We show how this algebra arises naturally from the three-dimensional geometry of factorization of correlators of bulk fields on the disk. This allows us to derive explicit expressions for the structure constants of the classifying algebra as invariants of ribbon graphs in the three-manifold S^2 x S^1. Our result unravels a precise relation between intertwiners of the action of the mapping class group on spaces of conformal blocks and boundary conditions in rational conformal field theories.
Fuchs J"urgen
Schweigert Christoph
Stigner Carl
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