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Open/Closed BPS Correspondence and Integrality

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arxiv 2307.13542 v3 pith:ZELBIIIJ submitted 2023-07-25 math.AG hep-thmath.SG

Song Yu This is my paper · ORCID
classification math.AGhep-thmath.SG
keywords invariantsopenintegralitycalabi-yauclosedcorrespondencefoldsgromov-witten
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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.

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  1. Link in $\mathbb{R}\mathbb{P}^3$ and the Topological Vertex

    math-ph 2025-01 conditional novelty 6.0 of 10

    First topological-vertex computations of colored unknot and Hopf link invariants in RP^3 yield power series with positive integer q-expansions, conjecturally the Poincare series of a new link homology.

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