Torus structure on graphs and twisted partition functions for minimal and affine models

TL;DR

This paper explores the classification of twisted partition functions in conformal field theory using Ocneanu quantum geometry, focusing on ADE diagrams and their applications to affine, minimal, WZW, Virasoro, and W_{3} models.

Contribution

It introduces a novel approach to classify twisted partition functions via Ocneanu quantum geometry of ADE diagrams, extending to higher Coxeter-Dynkin systems.

Findings

Classification of twisted partition functions for various models

Application of Ocneanu quantum geometry to conformal field theory

Examples involving WZW, Virasoro, and W_{3} models

Abstract

Using the Ocneanu quantum geometry of ADE diagrams (and of other diagrams belonging to higher Coxeter-Dynkin systems), we discuss the classification of twisted partition functions for affine and minimal models in conformal field theory and study several examples associated with the WZW, Virasoro and W_{3} cases.