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

## TL;DR

The paper introduces a novel method to compute the K"ahler potential of Calabi-Yau moduli spaces by leveraging their relation to Frobenius manifolds and Landau-Ginzburg models, enhancing understanding of string compactifications.

## Contribution

It presents a new procedure for calculating the K"ahler potential of CY moduli spaces, specifically for hypersurfaces in weighted projective spaces, connecting them to Frobenius manifolds.

## Key findings

- New computational method for K"ahler potential
- Links CY moduli spaces to Frobenius manifolds
- Applicable to hypersurfaces in weighted projective spaces

## Abstract

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.