All genus open mirror symmetry for the projective line

2025/07/21 by Jinghao Yu, Yu, Jinghao, Zhengyu Zong +1 · 1 citation
Mathematics · Physics and Astronomy · #Algebraic Geometry (math.AG) #FOS: Mathematics #FOS: Physical sciences #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #Symplectic Geometry (math.SG)

paper · pdf · doi:10.48550/arxiv.2507.15187

openalex publication_date 2025/07/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that the Chekhov-Eynard-Orantin recursion on the mirror curve of ℙ¹ encodes all genus equivariant open Gromov-Witten invariants of (ℙ¹, ℝℙ¹). This result can be viewed as an all genus equivariant open mirror symmetry for (ℙ¹, ℝℙ¹).

Citations

• Structure of Higher Genus Gromov-Witten Invariants of Quintic 3-folds
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• Invariants of algebraic curves and topological expansion
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• Mirror Principle III
• Mirror Principle I
• A mirror theorem for toric complete intersections
• Equivariant Gromov - Witten Invariants

Cited by

• Mirror symmetry and open/closed correspondence for the projective line

Related

• Mirror Symmetry for Closed, Open, and Unoriented Gromov-Witten\n Invariants
• Mirror symmetry and open/closed correspondence for the projective line
• Relative Gromov-Witten invariants and the mirror formula
• Genus one mirror symmetry for intersection of two cubics in ℙ⁵
• A mirror theorem for genus two Gromov-Witten invariants of quintic threefolds