A Note On ADE String Compactifications

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We address the question whether so-called m-invariants of the N=2 super Virasoro algebra can be used for the construction of reasonable four-dimensional string models. It turns out that an infinite subset of those are pathological in the sense that - although N=2 supersymmetric - the Ramond sector is not isomorphic to the Neveu-Schwarz sector. Consequently, these two properties are independent and only requiring both guarantees an N=1 space-time supersymmetric string spectrum. However, the remaining 529 consistent spectra - 210 of them are mirrors of Gepner models and 76 real orbifolds - show exact mirror symmetry and are contained in a recent classification of orbifolds of Gepner models.