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Unitarity of rationalN = 2 superconformal theories

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Abstract

We demonstrate that all rational models of theN = 2 super Virasoro algebra are unitary. Our arguments are based on three different methods: we determine Zhu’s algebraA(H0) (for which we give a physically motivated derivation) explicitly for certain theories, we analyse the modular properties of some of the vacuum characters, and we use the coset realisation of the algebra in terms ofsu(2) and two free fermions. Some of our arguments generalise to the Kazama-Suzuki models indicating that all rationalN = 2 supersymmetric models might be unitary.

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

    W. Eholzer & M. R. Gaberdiel

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  1. W. Eholzer
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  2. M. R. Gaberdiel
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Correspondence to W. Eholzer or M. R. Gaberdiel.

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Eholzer, W., Gaberdiel, M.R. Unitarity of rationalN = 2 superconformal theories. Commun. Math. Phys. 186, 61–85 (1997). https://doi.org/10.1007/BF02885672

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