Symmetry, Integrability and Geometry: Methods and Applications (Apr 2009)
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 E_4, E_6 and E_8 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 groupoïds.
