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Vertex operators for non-simply-laced algebras

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Abstract

A vertex operator construction is given for the level one representations of the affine Kac-Moody algebras associated with non-simply-laced finite-dimensional Lie algebras, using free boson and interacting fermion fields. The fermion fields are constructed explicitly and a detailed discussion is given of the theory of the cocycles necessary for this and other vertex operator constructions. The construction is related in detail to the folding of Dynkin diagrams and a generalisation of it yields Freudenthal's magic square.

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Authors and Affiliations

  1. Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, CB3 9EW, Cambridge, United Kingdom

    P. Goddard

  2. Physikalisches Institut, Universität Bonn, Nussallee 12, D-5300, Bonn 1, Germany

    W. Nahm

  3. Blackett Laboratory, Imperial College, SW7 2BZ, London, U.K.

    D. Olive

  4. Laboratoire de Physique Theorique de L'Ecole Normale Superieure, 24 Rue Lhomond, F-75231, Paris Cedex 05, France

    A. Schwimmer

Authors
  1. P. Goddard
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  2. W. Nahm
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  3. D. Olive
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  4. A. Schwimmer
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Additional information

Communicated by A. Jaffe

On leave from the Weizmann Institute, Israel

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Goddard, P., Nahm, W., Olive, D. et al. Vertex operators for non-simply-laced algebras. Commun.Math. Phys. 107, 179–212 (1986). https://doi.org/10.1007/BF01209391

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  • DOI: https://doi.org/10.1007/BF01209391

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