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Level 1 WZW superselection sectors

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Abstract

The superselection structure of the Wess-Zumino-Witten theory based on the affine Lie algebra\(\widehat{so}(N)\) at level one is investigated for arbitraryN. By making use of the free fermion representation of the affine algebra, the endomorphisms which represent the superselection sectors on the observable algebra can be constructed as endomorphisms of the underlying Majorana algebra. These endomorphisms do not close on the chiral algebra of the theory, but we are able to obtain a larger algebra on which the endomorphisms close. The composition of equivalence classes of the endomorphisms reproduces the WZW fusion rules.

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Author notes

  1. Alexander Ganchev

    Present address: Institute for Nuclear Research and Nuclear Energy, boul. Trakia, 72, Sofia, bulgaria

Authors and Affiliations

  1. Theory Division, CERN, CH-1211, Genève 23, Switzerland

    Jürgen Fuchs, Alexander Ganchev & Peter Vecsernyés

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  1. Jürgen Fuchs
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  2. Alexander Ganchev
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  3. Peter Vecsernyés
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Communicated by J. Fröhlich

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Fuchs, J., Ganchev, A. & Vecsernyés, P. Level 1 WZW superselection sectors. Commun.Math. Phys. 146, 553–583 (1992). https://doi.org/10.1007/BF02097016

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  • DOI: https://doi.org/10.1007/BF02097016

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