A new approach for computing the geometry of the moduli spaces for a Calabi-Yau manifold

Understand

It is known that moduli spaces of Calabi-Yau (CY) manifolds are special K\"ahler manifolds.

• This structure determines the corresponding low-energy effective theory which arises in superstring compactifications on CY manifolds.
• In the case, where CY manifold is given as a hypersurface in the weighted projective space, we propose a new procedure for computing the K\"ahler potential of the moduli space.
• Our method is based on the fact that the moduli space of CY manifolds is a marginal subspace of the Frobenius manifold which arises on the deformation space of the corresponding Landau--Ginzburg superpotential.