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Categorification and correlation functions in conformal field theory

Ingo Runkel·Jurgen Fuchs·Christoph Schweigert
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Abstract

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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Ingo Runkel, Jurgen Fuchs, Christoph Schweigert. 2006-02-05. Categorification and correlation functions in conformal field theory. https://arxiv.org/abs/math/0602079

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