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The W N Minimal Model Classification

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Abstract

We first rigourously establish, for any N ≥ 2, that the toroidal modular invariant partition functions for the (not necessarily unitary) W N (p, q) minimal models biject onto a well-defined subset of those of the SU(N) × SU(N) Wess-Zumino-Witten theories at level (p − N, q − N). This permits considerable simplifications to the proof of the Cappelli-Itzykson-Zuber classification of Virasoro minimal models. More important, we obtain from this the complete classification of all modular invariants for the W 3(p, q) minimal models. All should be realised by rational conformal field theories. Previously, only those for the unitary models, i.e. W 3(p, p + 1), were classified. For all N our correspondence yields for free an extensive list of W N (p, q) modular invariants. The W 3 modular invariants, like the Virasoro minimal models, all factorise into SU(3) modular invariants, but this fails in general for larger N. We also classify the SU(3) × SU(3) modular invariants, and find there a new infinite series of exceptionals.

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Authors and Affiliations

  1. Mathematics Department, Grant MacEwan University, 10700-104 Ave, Edmonton, AB, T5J 4S2, Canada

    Elaine Beltaos

  2. Mathematics Department, University of Alberta, Edmonton, AB, T6G 2G1, Canada

    Terry Gannon

Authors
  1. Elaine Beltaos
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  2. Terry Gannon
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Correspondence to Terry Gannon.

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Communicated by Y. Kawahigashi

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Beltaos, E., Gannon, T. The W N Minimal Model Classification. Commun. Math. Phys. 312, 337–360 (2012). https://doi.org/10.1007/s00220-012-1473-4

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  • DOI: https://doi.org/10.1007/s00220-012-1473-4

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