The requirement the space-time supersymmetry in the String theory is equivalent to the geometrical condition of the compactification six dimensions on Calabi-Yau (CY) threefold. The massless sector of the Superstring theory after the compactification on CY is physically the most important. The properties of the Effective Lagrangian of the corresponding model, which describes this sector, are defined in terms of the Special Kahler geometry on CY moduli space. We suggest a new approach for computing the Special geometry based on the relation to the Landau-Ginzburg superpotential of the model with a Frobenius manifold structure.

Landau Institute of Theoretical Physics