Categorification and correlation functions in conformal field theory

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.

16 pages, Invited contribution to the ICM 2006

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Cited by in corpus (22)

• Duality and defects in rational conformal field theory
• Virasoro representations and fusion for general augmented minimal models
• More Morphisms between Bundle Gerbes
• Invertible defects and isomorphisms of rational CFTs
• Traces on Module Categories over Fusion Categories
• A geometric approach to boundaries and surface defects in Dijkgraaf-Witten theories
• Bogomolov multiplier, double class-preserving automorphisms and modular invariants for orbifolds
• The fusion algebra of bimodule categories
• Twenty-five years of two-dimensional rational conformal field theory
• Full field algebras, operads and tensor categories
• Bundle Gerbes and Surface Holonomy
• Conformal nets III: fusion of defects
• Defects in G/H coset, G/G topological field theory and discrete Fourier-Mukai transform
• On duality and extended chiral symmetry in the SL(2,R) WZW model
• Full Logarithmic Conformal Field theory - an Attempt at a Status Report
• Algebraic structures in comodule categories over weak bialgebras
• Conformal Field Theories as Scaling Limit of Anyonic Chains
• Survey of mathematical foundations of QFT and perturbative string theory
• Modular invariants for group-theoretical modular data. I
• The Operator Product Expansion in Quantum Field Theory
• Permutation actions on modular tensor categories of topological multilayer phases
• The universality question for noncommutative quantum field theory