Open/Closed BPS Correspondence and Integrality

TL;DR

This paper proves the integrality and finiteness of open BPS invariants for toric Calabi-Yau 3-folds and extends the open/closed Gromov-Witten correspondence to BPS invariants, also establishing integrality for certain genus-zero invariants of toric Calabi-Yau 4-folds.

Contribution

It establishes the integrality and finiteness of open BPS invariants and extends the open/closed Gromov-Witten correspondence to BPS invariants for toric Calabi-Yau manifolds.

Findings

Proved integrality and finiteness of open BPS invariants.

Extended open/closed Gromov-Witten correspondence to BPS invariants.

Established integrality of genus-zero BPS invariants of toric Calabi-Yau 4-folds.

Abstract

We prove the integrality and finiteness of open BPS invariants of toric Calabi-Yau 3-folds relative to Aganagic-Vafa outer branes, defined from open Gromov-Witten invariants by the Labastida-Mari\~no-Ooguri-Vafa formula. Specializing to disk invariants, we extend the open/closed correspondence of Gromov-Witten invariants to BPS invariants and prove the integrality of a class of genus-zero BPS invariants of toric Calabi-Yau 4-folds, thereby providing additional examples for the conjecture of Klemm-Pandharipande.