RCFT with defects: Factorization and fundamental world sheets

TL;DR

This paper extends the understanding of rational conformal field theories by demonstrating that correlation functions with defect lines still satisfy key properties like factorization, and that all correlators can be derived from fundamental ones.

Contribution

It generalizes the factorization and fundamental correlator results to oriented world sheets with topological defect lines in rational conformal field theories.

Findings

Correlation functions satisfy locality, modular invariance, and factorization with defects.

All correlators are related to a small set of fundamental correlators.

The results apply to world sheets with arbitrary networks of topological defect lines.

Abstract

It is known that for any full rational conformal field theory, the correlation functions that are obtained by the TFT construction satisfy all locality, modular invariance and factorization conditions, and that there is a small set of fundamental correlators to which all others are related via factorization - provided that the world sheets considered do not contain any non-trivial defect lines. In this paper we generalize both results to oriented world sheets with an arbitrary network of topological defect lines.