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

摘要

It is known that moduli spaces of Calabi-Yau (CY) manifolds are specialK\"ahler manifolds. This structure determines the corresponding low-energyeffective theory which arises in superstring compactifications on CY manifolds.In the case, where CY manifold is given as a hypersurface in the weightedprojective space, we propose a new procedure for computing the K\"ahlerpotential of the moduli space. Our method is based on the fact that the modulispace of CY manifolds is a marginal subspace of the Frobenius manifold whicharises on the deformation space of the corresponding Landau--Ginzburgsuperpotential.