Type II/F-theory Superpotentials and Ooguri-Vafa Invariants of Compact Calabi-Yau Threefolds with Three Deformations

TL;DR

This paper computes D-brane superpotentials and Ooguri-Vafa invariants for specific Calabi-Yau threefolds using hypergeometric GKZ systems and mirror symmetry, linking F-theory flux superpotentials with open Gromov-Witten invariants.

Contribution

It introduces a method to calculate superpotentials and invariants for Calabi-Yau threefolds with three deformations using GKZ systems and mirror symmetry.

Findings

Explicit superpotential calculations for two Calabi-Yau manifolds.

Derivation of Ooguri-Vafa invariants from A-model expansion.

Connection between flux superpotentials and open Gromov-Witten invariants.

Abstract

We calculate the D-brane superpotentials for two Calabi-Yau manifolds with three deformations by the generalized hypergeometric GKZ systems, which give rise to the flux superpotentials $\mathcal{W}_{GVW}$ of the dual F-theory compactification on the relevant Calabi-Yau fourfolds in the weak decoupling limit. We also compute the Ooguri-Vafa invariants from A-model expansion with mirror symmetry, which are related to the open Gromov-Witten invariants.