Boundary conformal field theories and loop models

TL;DR

This paper introduces a systematic method to derive conformal loop models from rational CFTs using fusion matrices, applicable to minimal models, dilute O(n) models, and WZW SU(2) models, respecting boundary conditions.

Contribution

The authors develop a novel approach to construct boundary conformal loop models from rational CFTs via ADE models and fusion matrices, unifying various examples including minimal, O(n), and WZW models.

Findings

Loop models derived for minimal CFTs

Dilute O(n) loop models on square lattices analyzed

Proposals for WZW SU(2) models presented

Abstract

We propose a systematic method to extract conformal loop models for rational conformal field theories (CFT). Method is based on defining an ADE model for boundary primary operators by using the fusion matrices of these operators as adjacency matrices. These loop models respect the conformal boundary conditions. We discuss the loop models that can be extracted by this method for minimal CFTs and then we will give dilute O(n) loop models on the square lattice as examples for these loop models. We give also some proposals for WZW SU(2) models.