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W-Algebras, new rational models and completeness of thec=1 classification

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Abstract

Two series ofW with two generators are constructed from chiral vertex operators of a free field representation. Ifc=1–24k, there exists aW(2, 3k) algebra for k ∈ ℤ+/2 and aW(2, 8k) algebra for k ∈ ℤ+/4. All possible lowest-weight representations, their characters and fusion rules are calculated proving that these theories are rational. It is shown, that these non-unitary theories complete the classification of all rational theories with effective central chargec eff=1. The results are generalized to the case of extended supersymmetric conformal algebras.

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  1. Physikalisches Institut, Universität Bonn, Nussallee 12, D-53115, Bonn, Germany

    Michael Flohr

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  1. Michael Flohr
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Communicated by N. Yu. Reshetikhin

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Flohr, M. W-Algebras, new rational models and completeness of thec=1 classification. Commun.Math. Phys. 157, 179–212 (1993). https://doi.org/10.1007/BF02098024

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