D-brane Superpotentials and Geometric Invariants in Complete Intersection Calabi-Yau Manifolds

TL;DR

This paper investigates B-brane superpotentials and Ooguri-Vafa invariants in complete intersection Calabi-Yau threefolds by using blow-up techniques and mirror symmetry, linking geometric invariants to physical superpotentials.

Contribution

It introduces a method to compute brane superpotentials and invariants via blow-up of ambient spaces and period integrals, advancing understanding of D-branes in Calabi-Yau manifolds.

Findings

Expressed B-brane superpotentials as period integrals of blow-up manifolds.

Linked superpotentials to Ooguri-Vafa invariants through mirror maps.

Provided a geometric framework for counting holomorphic disks.

Abstract

By blowing up the ambient space along the curve wrapped by B-branes, we study the brane superpotentials and Ooguri-Vafa invariants on complete intersections Calabi-Yau threefolds. On the topological B-model side, B-brane superpotentials are expressed in terms of the period integral of the blow-up manifolds. By mirror maps, the superpotentials are generating functions of Ooguri-Vafa invariants counting holomorphic disks on the topological A-model side.