Multi-Component Open/Relative/Local Correspondence

2025/12/17 by Yu, Song, Zhang, Ke, Zong, Zhengyu
Mathematics · #Algebraic Geometry and Number Theory #Advanced Combinatorial Mathematics #Geometric and Algebraic Topology

paper · doi:10.48550/arxiv.2512.15074

Abstract

For a toric Calabi-Yau 3-orbifold relative to s Aganagic-Vafa outer branes, we prove a correspondence among the genus-zero open Gromov-Witten invariants with maximal winding at each brane and: (i) closed invariants of a toric Calabi-Yau (3+s)-orbifold; (ii) formal relative invariants of a formal toric Calabi-Yau (FTCY) 3-orbifold with maximal tangency to s divisors; (iii) formal relative invariants of a sequence of FTCY intermediate geometries interpolating dimensions 3 and 3+s. The correspondence provides examples of the log/local principle of van Garrel-Graber-Ruddat in the multi-component setting and the refined conjecture of Brini-Bousseau-van Garrel via intermediate geometries. It also establishes the multi-component case of the open/closed correspondence proposed by Lerche-Mayr and studied by Liu-Yu. As an application, we obtain examples of the conjecture of Klemm-Pandharipande on the integrality of BPS invariants of higher-dimensional toric Calabi-Yau manifolds. Along the way, we set the basic stages of the relative Gromov-Witten theory of higher-dimensional FTCY orbifolds, generalizing the case of smooth 3-folds by Li-Liu-Liu-Zhou.

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Related

• A relation for Gromov-Witten invariants of local Calabi-Yau threefolds
• Orbifold Open/Closed Correspondence and Mirror Symmetry
• Open Gromov-Witten theory on Calabi-Yau three-folds I
• Relative Gromov-Witten invariants and the enumerative meaning of mirror maps for toric Calabi-Yau orbifolds
• The open string McKay correspondence for type A singularities