Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 5 (2009), 044, 31 pages      arXiv:0805.4678      https://doi.org/10.3842/SIGMA.2009.044

Quantum Symmetries for Exceptional SU(4) Modular Invariants Associated with Conformal Embeddings

Robert Coquereaux and Gil Schieber
Centre de Physique Théorique (CPT), Luminy, Marseille, France

Received December 24, 2008, in final form March 31, 2009; Published online April 12, 2009

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, E6 and E8 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.

Key words: quantum symmetries; modular invariance; conformal field theories.

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