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This article is cited in 9 scientific papers (total in 9 papers)
Quantum Symmetries for Exceptional $\mathrm{SU}(4)$ Modular Invariants Associated with Conformal Embeddings
Robert Coquereaux, Gil Schieber Centre de Physique Théorique (CPT), Luminy, Marseille, France
Abstract:
Three exceptional modular invariants of $\mathrm{SU}(4)$ 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 $\mathcal E_4$, $\mathcal E_6$ and $\mathcal E_8$ describing exceptional quantum subgroups of type $\mathrm{SU}(4)$. We also obtain characteristic numbers (quantum cardinalities, dimensions) for each of them and for their associated quantum groupoïds.
Keywords:
quantum symmetries; modular invariance; conformal field theories.
Received: December 24, 2008; in final form March 31, 2009; Published online April 12, 2009
Citation:
Robert Coquereaux, Gil Schieber, “Quantum Symmetries for Exceptional $\mathrm{SU}(4)$ Modular Invariants Associated with Conformal Embeddings”, SIGMA, 5 (2009), 044, 31 pp.
Linking options:
https://www.mathnet.ru/eng/sigma390 https://www.mathnet.ru/eng/sigma/v5/p44
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Abstract page: | 221 | Full-text PDF : | 50 | References: | 33 |
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