RCFT with defects: Factorization and fundamental world sheets
Jens Fjelstad, Jurgen Fuchs, Carl Stigner
TL;DR
The paper extends the TFT-based factorization framework for full rational conformal field theories to oriented world sheets with arbitrary networks of topological defect lines. It proves a bulk factorization identity across defect-laden cuts, expressing any correlator $C(\varSigma)$ as a finite sum over defect labels and disorder insertions using a defect-aware gluing map $G\ell_{pq}$, with precise coefficients tied to defect two-point data. A rigorous world-sheet framework is developed, defining decorated defect graphs and a suite of equivalences (including intrinsic and graph-based moves) that reduce correlators to a finite set of fundamental defect-containing world sheets; modular covariance is established, ensuring correlators transform coherently under mapping class group actions. The results connect to the TFT construction via surgery relations and provide a practical, finite basis for correlators in defective RCFTs, with potential applications in condensed matter and QFT contexts where defect networks arise.
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.