K\"ahler Potential of Moduli Space of Calabi-Yau $d$-fold embedded in $CP^{d+1}$

Abstract

We study a kaehler potential K of a one parameter family of Calabi-Yau d-fold embedded in CP^{d+1}. By comparing results of the topological B-model and the data of the CFT calculation at Gepner point, the K is determined unambiguously. It has a moduli parameter psi that describes a deformation of the CFT by a marginal operator. Also the metric, curvature and hermitian two-point functions in the neighborhood of the Gepner point are analyzed. We use a recipe of tt^{*} fusion and develop a method to determine the K from the point of view of topological sigma model. It is not restricted to this specific model and can be applied to other Calabi-Yau cases.