The classifying algebra for defects
arXiv:1007.0401 · doi:10.1016/j.nuclphysb.2010.10.008
Abstract
We demonstrate that topological defects in a rational conformal field theory can be described by a classifying algebra for defects - a finite-dimensional semisimple unital commutative associative algebra whose irreducible representations give the defect transmission coefficients. We show in particular that the structure constants of the classifying algebra are traces of operators on spaces of conformal blocks and that the defect transmission coefficients determine the defect partition functions.
47 pages, several figures. v2: ref. [13] added; comparison of results with those of ref. [18] added (pages 15 and 34) v3: comment on the folding trick added at the end of section 2, typos corrected