Open/Closed BPS Correspondence and Integrality

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-Mariño-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.

29 pages, 2 figures

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Cited by in corpus (2)

• The log-open correspondence for two-component Looijenga pairs
• Open WDVV Equations and Frobenius Structures for Toric Calabi-Yau 3-Folds