Quantum symmetries for exceptional SU(4) modular invariants associated with conformal embeddings

TL;DR

This paper investigates exceptional SU(4) modular invariants at levels 4, 6, and 8, deriving quantum symmetry algebras, generators, and associated graphs from conformal embeddings, enriching the understanding of quantum subgroups and their invariants.

Contribution

It introduces a method to determine quantum symmetry algebras and graphs for exceptional SU(4) invariants using conformal embeddings, providing new insights into quantum subgroups.

Findings

Derived quantum symmetry algebras and generators for each invariant.

Reconstructed known graphs E4, E6, E8 for SU(4).

Computed quantum cardinalities and dimensions for the quantum groupoids.

Abstract

Three exceptional modular invariants of SU(4) exist at levels 4, 6 and 8. They can be obtained from appropriate conformal embeddings and the corresponding graphs have self-fusion. From these embeddings, or from their associated modular invariants, we determine the algebras of quantum symmetries, obtain their generators, and, as a by-product, recover the known graphs E4(SU4), E6(SU4) and E8(SU4) describing exceptional quantum subgroups of type SU(4). We also obtain characteristic numbers (quantum cardinalities, dimensions) for each of them and for their associated quantum groupoids.