On the complete classification of the unitary N=2 minimal superconformal field theories

TL;DR

This paper completes the classification of unitary N=2 minimal superconformal field theories by showing all modular invariants correspond to actual models, confirming conjectures about their construction via orbifolds.

Contribution

It proves that every modular invariant candidate for unitary N=2 minimal models is realized by an actual model, confirming a conjecture about their orbifold construction.

Findings

All modular invariants correspond to actual models.

Existence of models for every allowed partition function.

Confirmation of simple current invariants as orbifolds of diagonal models.

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 of a partition function for such a theory is indeed the partition function of a minimal model. A family of models constructed via orbifoldings of either the diagonal model or of the space-time supersymmetric exceptional models 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. Kreuzer and Schellekens' conjecture 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.