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

Robert Coquereaux (1, 2, 3) , Gil Schieber (2, 3)

1 CPT - E2 Géométrie, Physique et Symétries
2 CPT - Centre de Physique Théorique - UMR 6207
3 CPT - Centre de Physique Théorique - UMR 7332

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.

Mots clés: quantum symmetries; modular invariance; conformal field theories

Domaines: Algèbres quantiques [math.QA]; Physique mathématique [math-ph]; Physique mathématique [math-ph]; Physique des Hautes Energies - Théorie [hep-th]

Robert Coquereaux, Gil Schieber. Quantum symmetries for exceptional SU(4) modular invariants associated with conformal embeddings. Symmetry, Integrability and Geometry : Methods and Applications, 2009, 5 (044), http://www.emis.de/journals/SIGMA/2009/044/. ⟨10.3842/SIGMA.2009.044⟩. ⟨hal-00283368v3⟩