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

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.

33 pages, 3 color figures

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• Notes on TQFT Wire Models and Coherence Equations for SU(3) Triangular Cells
• Essential paths space on ADE SU(3) graphs: A geometric approach
• SU(3) higher roots and their lattices
• Type $II$ quantum subgroups of ${\mathfrak{sl}}_N$. $I$: Symmetries of local modules