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

Abstract

It is known that moduli spaces of Calabi–Yau (CY) manifolds are special Kähler manifolds. This structure determines the corresponding low-energy effective theory which arises in superstring compactifications on CY manifolds. In the case where a CY manifold is given as a hypersurface in the weighted projective space, we propose a new procedure for computing the Kähler 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.