Superpotentials of D-branes in Calabi-Yau Manifolds with Several Moduli by Mirror Symmetry and Blown-up

TL;DR

This paper computes B-brane superpotentials in Calabi-Yau manifolds with multiple moduli by using blow-up techniques and mirror symmetry, providing explicit examples and invariants.

Contribution

It introduces a method to calculate superpotentials with several moduli via blow-up and mirror symmetry, extending previous single-moduli approaches.

Findings

Explicit superpotential calculations for specific Calabi-Yau examples

Extraction of Ooguri-Vafa invariants from the superpotentials

Demonstration of the blow-up method in the context of multiple moduli

Abstract

We study B-brane superpotentials depending on several closed- and open- moduli on Calabi-Yau hypersurfaces and complete intersections. By blowing up the ambient space along a curve wrapped by B-branes in a Calabi-Yau manifold, we obtain a blow-up new manifold and the period integral satisfying the GKZ-system. Via mirror symmetry to A-model, we calculate the superpotentials and extract Ooguri-Vafa invariants for concrete examples of several open-closed moduli in Calabi-Yau manifolds.