The Asymmetric CFT Landscape in D=4,6,8 with Extended Supersymmetry

We study asymmetric simple-current extensions of Gepner models in dimensions $D=4,6,8$ with at least eight supercharges in the right-moving sector. The models obtained in an extensive stochastic computer search belong to a small number of different classes. These classes can be categorized as dimensional reductions, asymmetric orbifolds with $(-1{)}^{F_L}$, extra gauge enhancement and as coming from the super Higgs-effect. Models in the latter class are particularly interesting, as they may correspond to non-geometric flux compactifications.