Categorification and correlation functions in conformal field theory

TL;DR

This paper develops a 2-categorical framework using Frobenius algebras and bimodules within modular tensor categories to systematically construct correlation functions in two-dimensional rational conformal field theories.

Contribution

It introduces a novel 2-category structure that captures the algebraic and categorical data necessary for conformal field theory correlation functions.

Findings

Provides a categorical construction for all correlation functions

Interprets bimodules as physical entities like boundary conditions and defects

Establishes a link between algebraic structures and physical features in CFT

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.