A note on ADE string compactifications

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