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Categorification and correlation functions in conformal field theory
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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.
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Rational and non-rational two-dimensional conformal field theories arising from lattices
Even lattices in an indefinite bilinear form classify two-dimensional conformal net extensions of Heisenberg nets under a discreteness assumption, with explicit rational and non-rational examples.
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