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Galois modular invariants of WZW models. (English) Zbl 1052.81530

Summary: The set of modular invariants that can be obtained from Galois transformations is investigated systematically for WZW models. It is shown that a large subset of Galois modular invariants coincides with simple current invariants. For algebras of type B and D infinite series of previously unknown exceptional automorphism invariants are found.

MSC:

81R10 Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, \(W\)-algebras and other current algebras and their representations
11F22 Relationship to Lie algebras and finite simple groups
11Z05 Miscellaneous applications of number theory
17B68 Virasoro and related algebras
81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics
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