Conformal boundary conditions and three-dimensional topological field theory

TL;DR

This paper develops a comprehensive method to compute correlation functions in 2D rational conformal field theories using Wilson graphs in three-manifolds, ensuring modular invariance and proper factorization.

Contribution

It introduces a general construction for all correlators in 2D rational CFTs using topological methods involving Wilson graphs in three-manifolds.

Findings

Correlation functions expressed via Wilson graphs

Ensures modular invariance of correlators

Satisfies factorization rules

Abstract

We present a general construction of all correlation functions of a two-dimensional rational conformal field theory, for an arbitrary number of bulk and boundary fields and arbitrary topologies. The correlators are expressed in terms of Wilson graphs in a certain three-manifold, the connecting manifold. The amplitudes constructed this way can be shown to be modular invariant and to obey the correct factorization rules.