LANDAU-GINZBURG STRING VACUA

We classify (2,2) supersymmetric string vacua which are represented as Landau-Ginzburg theories, with a quasihomogeneous potential that has an isolated singularity at the origin. There are at least three thousand distinct models in this class, All vacua of this type lead to Euler numbers lying in the range -960 less-than-or-equal-to X less-than-or-equal-to 960. The Euler characteristics do not pair up completely; hence the space of Landau-Ginzburg ground states is not mirror-symmetric even though it exhibits a high degree of symmetry. We discuss in some detail the relation between Landau-Ginzburg models and Calabi-Yau manifolds and describe a subtlety regarding Landau-Ginzburg potentials with an arbitrary number of fields. We also show that the use of topological identities makes it possible to relate Landau-Ginzburg theories to types of Calabi-Yau manifolds for which the usual Landau-Ginzburg framework does not apply.