Boundary conformal field theories and loop models

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.

23 Pages, major changes! title changed

References in corpus (14)

• Conformal radii for conformal loop ensembles
• SLE_k growth processes and conformal field theories
• Conformal boundary loop models
• Discretely Holomorphic Parafermions and Integrable Loop Models
• A Line of Critical Points in 2+1 Dimensions: Quantum Critical Loop Gases and Non-Abelian Gauge Theory
• Conformal two-boundary loop model on the annulus
• SLE in the three-state Potts model - a numerical study
• Stochastic Loewner evolution for conformal field theories with Lie-group symmetries
• The O(n) model on the annulus
• Loop models and their critical points
• Consistent superconformal boundary states
• Critical points in coupled Potts models and critical phases in coupled loop models
• ADE and SLE
• Loop models for CFTs