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The branching rules of conformal embeddings

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Abstract

After recalling the main properties of a conformal embedding of Lie algebrasg⊃p, which is defined by the equality of the Sugawara central charges on both sides, we launch a systematic study of their branching rules. The bulk of the paper is devoted to the proof of a general formula in the casesu(mn) 1⊃su(m) n⊕su(n) m. At the end we give some applications to the construction of modular invariant partition functions.

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Authors and Affiliations

  1. Service de Physique Théorique, Laboratoire de l'Institut de Recherche Fondamentale du Commissariat à l'Energie Atomique, CEN-Saclay, F-91191, Gif-sur-Yvette Cedex, France

    Daniel Altschuler, Michel Bauer & Claude Itzykson

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  1. Daniel Altschuler
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  2. Michel Bauer
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  3. Claude Itzykson
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Communicated by K. Gawedzki

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Altschuler, D., Bauer, M. & Itzykson, C. The branching rules of conformal embeddings. Commun.Math. Phys. 132, 349–364 (1990). https://doi.org/10.1007/BF02096653

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  • DOI: https://doi.org/10.1007/BF02096653

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