The classification of affine \(SU(3)\) modular invariant partition functions

DOI10.1007/BF02099776zbMath0806.17031arXivhep-th/9212060OpenAlexW3103914615MaRDI QIDQ1325583

Terry Gannon

Publication date: 26 May 1994

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/hep-th/9212060

zbMATH Keywords

conformal field theoryaffine Lie algebrascurrent Lie algebraWZNW modelsSU(3) modular invariant partition functions

Mathematics Subject Classification ID

Two-dimensional field theories, conformal field theories, etc. in quantum mechanics (81T40) Applications of Lie (super)algebras to physics, etc. (17B81) Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, (W)-algebras and other current algebras and their representations (81R10)

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Cites Work

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• Non-Abelian bosonization in two dimensions
• New exceptional modular invariant partition functions for simple Kac- Moody algebras
• Conformal embeddings, rank-level duality and exceptional modular invariants
• Fusion rules and modular transformations in 2D conformal field theory
• Classical and quantum conformal field theory
• \({\mathbb{Z}}/N{\mathbb{Z}}\) conformal field theories
• Modular transformations of SU(N) affine characters and their commutant
• The branching rules of conformal embeddings
• The supersymmetry index and the construction of modular invariants
• Modular invariant partition functions in two dimensions
• Implications of an arithmetical symmetry of the commutant for modular invariants.
• Partition functions for heterotic WZW conformal field theories.
• Modular invariants for affine SU(3){\^{\ }} theories at prime heights
• $\widehat{{\rm su}}\left( 3 \right)_k $ FUSION COEFFICIENTS
• THE LOW LEVEL MODULAR-INVARIANT PARTITION FUNCTIONS OF RANK-TWO ALGEBRAS
• G_N ⊗ G_L/G_N+L CONFORMAL FIELD THEORIES AND THEIR MODULAR INVARIANT PARTITION FUNCTIONS
• KAC-MOODY AND VIRASORO ALGEBRAS IN RELATION TO QUANTUM PHYSICS
• MODULAR INVARIANTS OF KAČ-MOODY ALGEBRAS FROM SELF-DUAL LATTICES
• Lie algebras associated with generalized Cartan matrices
• Level one Kac-Moody characters and modular invariance