Kähler potential of moduli space of Calabi–Yau d-fold embedded in CPd+1

Abstract

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