On the Complete Classification of Unitary N=2 Minimal Superconformal Field Theories

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 - - 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.