Loop models for CFTs

TL;DR

This paper introduces a method to associate loop models with primary operators in conformal field theories using fusion matrices, linking them to SLEs and applying to various CFT classes.

Contribution

It presents a novel approach to construct loop models from CFT data via fusion matrices, connecting them to SLEs and extending to multiple CFT types.

Findings

Loop models' weights are given by quantum dimensions.

Established a relationship between loop models and SLEs.

Applied method to WZW, minimal, and coset CFTs.

Abstract

By interpreting the fusion matrix as an adjacency matrix we associate a loop model to every primary operator of a generic conformal field theory. The weight of these loop models is given by the quantum dimension of the corresponding primary operator. Using the known results for the O(n) models we establish a relationship between these models and SLEs. The method is applied to WZW, $c<1$ minimal conformal field theories and other coset models.