2006/02/05 by Runkel, Ingo, Fuchs, Jurgen, Schweigert, Christoph
#18D10 #18D35 #81T40 #81T45 #Category Theory (math.CT) #FOS: Mathematics #Quantum Algebra (math.QA)
paper · doi:10.48550/arxiv.math/0602079
A modular tensor category provides the appropriate data for the construction of a three-dimensional topological field theory. We describe the following analogue for two-dimensional conformal field theories: a 2-category whose objects are symmetric special Frobenius algebras in a modular tensor category and whose morphisms are categories of bimodules. This 2-category provides sufficient ingredients for constructing all correlation functions of a two-dimensional rational conformal field theory. The bimodules have the physical interpretation of chiral data, boundary conditions, and topological defect lines of this theory.