Boundary conformal field theories and loop models

We propose a systematic method to extract conformal loop models for rational conformal field theories (CFT). The 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 give dilute O(n) loop models on the square lattice as examples for these loop models. We also give some proposals for WZW SU(2) models.