Correlation functions and boundary conditions in RCFT and three-dimensional topology

TL;DR

This paper develops a general method to construct correlation functions in rational conformal field theory on non-orientable surfaces with boundaries using 3D topological quantum field theory, ensuring they satisfy key consistency rules.

Contribution

It introduces a universal construction applicable to any modular category, linking RCFT correlation functions with 3D TQFT and explicitly calculating structure constants.

Findings

Correlation functions obey modular and factorization rules.

Structure constants are expressed in terms of modular category data.

Construction applies to non-orientable surfaces with boundary.

Abstract

We give a general construction of correlation functions in rational conformal field theory on a possibly non-orientable surface with boundary in terms of 3-dimensional topological quantum field theory. The construction applies to any modular category. It is proved that these correlation functions obey modular and factorization rules. Structure constants are calculated and expressed in terms of the data of the modular category.