Twisted partition functions for ADE boundary conformal field theories and Ocneanu algebras of quantum symmetries

TL;DR

This paper constructs explicit realizations of quantum symmetry algebras for ADE boundary conformal field theories using fusion algebras, and provides detailed twisted partition functions for each case.

Contribution

It offers a concrete realization of Ocneanu quantum symmetry algebras for all ADE diagrams within fusion algebra frameworks, along with explicit twisted partition functions.

Findings

Explicit realization of quantum symmetry algebras for ADE diagrams.

Complete list of twisted partition functions for each ADE case.

Connection between Ocneanu algebras and fusion graph algebras.

Abstract

For every ADE Dynkin diagram, we give a realization, in terms of usual fusion algebras (graph algebras), of the algebra of quantum symmetries described by the associated Ocneanu graph. We give explicitly, in each case, the list of the corresponding twisted partition functions