Special geometry on the moduli space for the two-moduli non-Fermat Calabi-Yau

TL;DR

This paper presents a method to compute the special Kähler metric on the moduli space of a two-moduli non-Fermat Calabi-Yau, utilizing Frobenius manifold structures, and applies it to an previously unknown case.

Contribution

It introduces a clarified computational method for the special Kähler metric on Calabi-Yau moduli spaces using Frobenius manifolds, applied to a new two-moduli non-Fermat example.

Findings

Successfully computed the special Kähler metric for the two-moduli non-Fermat Calabi-Yau.

Demonstrated the applicability of the method to previously uncharted moduli spaces.

Enhanced understanding of the geometric structure of non-Fermat Calabi-Yau moduli.

Abstract

We clarify the recently proposed method to compute a Special K\"ahler metric on a Calabi-Yau complex structures moduli space that uses the fact that the moduli space is a subspace of specific Frobenius manifold. We apply this method to computing the Special K\"ahler metric in a two-moduli non-Fermat model which has been unknown until now.