Calabi-Yau manifolds and N=2 superconformal firld theories

Abstract

The field configuration spaces of rescale invariant N=2 minimal supercon-formal theories are codimension one Ricci-flat submanifolds of a weighted complex projective space, or their products. The algebraic representations of the field configuration spaces for c=3,6,9 are obtained. It is shown that all codimension one Ricci-flat manifolds of a weighted complex projective space also correspond to the Gepner``s minimal tensor product models. In general, N=2 Landau-Ginzburg superconformal descriptions of string compactification are closely related to Calabi-Yau manifolds from complete intersections in products of weighted complex projective spaces ($WCP^n$). We have considered most general constructions of Calabi-Yau manifolds from complete intersections in products of $WCP^n$.