Determination of quantum symmetries for higher ADE systems from the modular T matrix

TL;DR

This paper develops a method to determine quantum symmetries of higher ADE systems using the modular T matrix, simplifying the analysis of boundary conformal field theories with defects.

Contribution

It introduces a novel approach to deduce quantum symmetries from the modular T matrix for higher ADE systems, extending known results for su(2) diagrams.

Findings

Quantum symmetries of su(2) diagrams are recovered.

Method applied to exceptional su(3) diagrams E5, E9, E21.

Provides a shortcut for twisted partition functions in boundary CFT.

Abstract

We show that the Ocneanu algebra of quantum symmetries, for an ADE diagram (or for higher Coxeter-Dynkin systems, like the Di Francesco - Zuber system) is, in most cases, deduced from the structure of the modular T matrix in the A series. We recover in this way the (known) quantum symmetries of su(2) diagrams and illustrate our method by studying those associated with the three genuine exceptional diagrams of type su(3), namely E5, E9 and E21. This also provides the shortest way to the determination of twisted partition functions in boundary conformal field theory with defect lines.