Loop models for conformal field theories

By interpreting the fusion matrix as an adjacency matrix we associate a loop model with 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.