Loop models for 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.

24 pages, 4 figures, published version, minor changes

References in corpus (5)

• 2D growth processes: SLE and Loewner chains
• Stochastic Loewner evolution for conformal field theories with Lie-group symmetries
• Loop models and their critical points
• SLE in self-dual critical Z(N) spin systems: CFT predictions
• ADE and SLE