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)(FL), extra gauge enhancement and as coming from the super Higgseffect. Models in the latter class are particularly interesting, as they may correspond to non-geometric flux compactifications.