Two-Sphere Partition Functions and Kähler Potentials on CY Moduli Spaces

We study the relation between exact partition functions of gauged N = (2, 2) linear sigma-models on S ² and Kähler potentials of Calabi-Yau manifolds proposed by Jockers et al. We suggest using a mirror version of this relation. For a class of manifolds given by Fermat hypersurfaces in weighted projective spaces, we check the relation by explicit calculation.