Mirror Symmetry, D-brane Superpotential and Ooguri-Vafa Invariants of Compact Calabi-Yau Manifolds

TL;DR

This paper computes B-brane superpotentials for specific compact Calabi-Yau hypersurfaces using GKZ systems, derives A-model superpotentials via mirror symmetry, and calculates Ooguri-Vafa invariants, advancing understanding of D-brane effects in string theory.

Contribution

It introduces a method to calculate D-brane superpotentials for non-Fermat type Calabi-Yau hypersurfaces using GKZ systems and derives related invariants through mirror symmetry.

Findings

Computed B-brane superpotentials for two non-Fermat Calabi-Yau hypersurfaces.

Derived A-model superpotentials and Ooguri-Vafa invariants for mirror manifolds.

Established a link between GKZ systems and D-brane superpotential calculations.

Abstract

The D-brane superpotential is very important in the low energy effective theory. As the generating function of all disk instantons from the worldsheet point of view, it plays a crucial role in deriving some important properties of the compact Calabi-Yau manifolds. By using the GKZ-generalized hypergeometric system, we will calculate the B-brane superpotentials of two non-fermat type compact Calabi-Yau hypersurfaces in toric varieties,respectively. Then according to the mirror symmetry, we obtain the A-model superpotentials and the Ooguri-Vafa invariants for the mirror Calabi-Yau manifolds.