On mirror symmetry in Wess–Zumino–Novikov–Witten models

We examine the problem of constructing $N=2$ superconformal algebras out of $N=1$ non-semi-simple affine Lie algebras. These $N=2$ superconformal theories share the property that the super Virasoro central charge depends only on the dimension of the Lie algebra. We find, in particular, a construction having a central charge $c=9$. This provides a possible internal space for string compactification and where mirror symmetry might be explored.