Abstract
Aiming at a complete classification of unitary N = 2 minimal models (where the assumption of space-time supersymmetry has been dropped), it is shown that each modular invariant candidate partition function of such a theory is indeed the partition function of a fully-fledged unitary N = 2 minimal model, subject to the assumptions that orbifolding is a ‘physical’ process and that the space-time supersymmetric \({\mathcal{A}}\) -\({\mathcal{D}}\) -\({\mathcal{E}}\) models are physical. A family of models constructed via orbifoldings of either the diagonal model or of the space-time supersymmetric exceptional models then demonstrates that there exists a unitary N = 2 minimal model for every one of the allowed partition functions in the list obtained from Gannon’s work (Gannon in Nucl Phys B 491:659–688, 1997).
Kreuzer and Schellekens’ conjecture (Nucl Phys B 411:97–121, 1994) that all simple current invariants can be obtained as orbifolds of the diagonal model, even when the extra assumption of higher-genus modular invariance is dropped, is confirmed in the case of the unitary N = 2 minimal models by simple counting arguments.
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Gray, O. On the Complete Classification of Unitary N = 2 Minimal Superconformal Field Theories. Commun. Math. Phys. 312, 611–654 (2012). https://doi.org/10.1007/s00220-012-1478-z
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DOI: https://doi.org/10.1007/s00220-012-1478-z