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.
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 SU(4) Modular Invariants Associated with Conformal Embeddings”, SIGMA, 5 (2009), 044, 31 pp.
\Bibitem{CoqSch09}
\by Robert Coquereaux, Gil Schieber
\paper Quantum Symmetries for Exceptional $\mathrm{SU}(4)$ Modular Invariants Associated with Conformal Embeddings
\jour SIGMA
\yr 2009
\vol 5
\papernumber 044
\totalpages 31
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https://www.mathnet.ru/eng/sigma390
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This publication is cited in the following 9 articles:
Cain Edie-Michell, “Type 𝐼𝐼 quantum subgroups of 𝔰𝔩_{𝔑}. ℑ: Symmetries of local modules”, Comm. Amer. Math. Soc., 3:3 (2023), 112
Robert Coquereaux, Applied and Numerical Harmonic Analysis, Theoretical Physics, Wavelets, Analysis, Genomics, 2023, 169
Komargodski Z., Ohmori K., Roumpedakis K., Seifnashri S., “Symmetries and Strings of Adjoint Qcd(2)”, J. High Energy Phys., 2021, no. 3, 103
Schopieray A., “Lie Theory For Fusion Categories: a Research Primer”, Topological Phases of Matter and Quantum Computation, Contemporary Mathematics, 747, eds. Bruillard P., Marrero C., Plavnik J., Amer Mathematical Soc, 2020, 1–26
Schopieray A., “Level Bounds For Exceptional Quantum Subgroups in Rank Two”, Int. J. Math., 29:5 (2018), 1850034
Coquereaux R., Zuber J.-B., “On sums of tensor and fusion multiplicities”, Journal of Physics A-Mathematical and Theoretical, 44:29 (2011), 295208
Robert Coquereaux, Esteban Isasi, Gil Schieber, “Notes on TQFT Wire Models and Coherence Equations for $SU(3)$ Triangular Cells”, SIGMA, 6 (2010), 099, 44 pp.
Coquereaux R., “Global dimensions for Lie groups at level $k$ and their conformally exceptional quantum subgroups”, Revista de La Union Matematica Argentina, 51:2 (2010), 17–42
Coquereaux R., Rais R., Tahri E.H., “Exceptional quantum subgroups for the rank two Lie algebras $B_2$ and $G_2$”, J. Math. Phys., 51:9 (2010), 092302, 34 pp.
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