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Conformal embeddings, rank-level duality and exceptional modular invariants

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Abstract

We compute the branching rules of the conformal embeddingsSO(4nk)1⊃Sp(2n) k ⊕Sp(2k) n andSO(rq) 1⊃SO(r) q ⊕SO(q) r forrq even. Using this we prove that the affine algebrasSp(2n) k andSp(2k) n have the sameS matrix and modular invariants. As a second application, we show how the triality ofSO(8) leads to an exceptional modular invariant forSU(2) at level 16 and for allSO(q≧4) at level 8.

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  1. Instituut voor Theoretische Fysica Celestijnenlaan 200 D, B-3001, Leuven, Belgium

    D. Verstegen

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  1. D. Verstegen
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Communicated by N. Yu. Reshetikhin

chargé de recherches du FNRS

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Verstegen, D. Conformal embeddings, rank-level duality and exceptional modular invariants. Commun.Math. Phys. 137, 567–586 (1991). https://doi.org/10.1007/BF02100278

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  • DOI: https://doi.org/10.1007/BF02100278

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