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Polynomial identities, indices, and duality for theN=1 superconformal modelSM(2, 4v)

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Abstract

We prove polynomial identities for theN=1 superconformal modelSM(2, 4v) which generalize and extend the known Fermi/Bose character identities. Our proof uses theq-trinomial coefficients of Andrews and Baxter on the bosonic side and a recently introduced very general method of producing recursion relations forq-series on the fermionic side. We use these polynomials to demonstrate a dual relation underq→q −1 betweenSM(2, 4v) andM(2v−1, 4v). We also introduce a genralization of the Witten index which is expressible in terms of the Rogers false theta functions.

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Authors and Affiliations

  1. Physikalisches Institut der RheinischenFriedrich-Wilhelms Universität Bonn, D-53115, Bonn, Germany

    Alexander Berkovich & Barry M. McCoy

  2. Institute for Theoretical Physics, State University of New York, 11794-3840, Stony Brook, New York

    William P. Orrick

Authors
  1. Alexander Berkovich
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  2. Barry M. McCoy
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  3. William P. Orrick
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Dedicated to the memory of Claude Itzykson.

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Berkovich, A., McCoy, B.M. & Orrick, W.P. Polynomial identities, indices, and duality for theN=1 superconformal modelSM(2, 4v). J Stat Phys 83, 795–837 (1996). https://doi.org/10.1007/BF02179546

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