All Genus Open-Closed Mirror Symmetry for Affine Toric Calabi-Yau 3-Orbifolds
Bohan Fang, Chiu-Chu Melissa Liu, Zhengyu Zong
TL;DR
This paper proves the Remodeling Conjecture, establishing a comprehensive all-genus open-closed mirror symmetry for affine toric Calabi-Yau 3-orbifolds, linking Gromov-Witten invariants to mirror curve invariants.
Contribution
It provides a proof of the Remodeling Conjecture for all genus open-closed Gromov-Witten invariants of affine toric Calabi-Yau 3-orbifolds, extending mirror symmetry to orbifold settings.
Findings
Proof of the Remodeling Conjecture for affine toric Calabi-Yau 3-orbifolds.
Establishment of all genus open-closed mirror symmetry in this context.
Connection between Gromov-Witten invariants and Eynard-Orantin invariants.
Abstract
The Remodeling Conjecture proposed by Bouchard-Klemm-Marino-Pasquetti [arXiv:0709.1453, arXiv:0807.0597] relates all genus open and closed Gromov-Witten invariants of a semi-projective toric Calabi-Yau 3-manifolds/3-orbifolds to the Eynard-Orantin invariants of the mirror curve of the toric Calabi-Yau 3-fold. In this paper, we present a proof of the Remodeling Conjecture for open-closed orbifold Gromov-Witten invariants of an arbitrary affine toric Calabi-Yau 3-orbifold relative to a framed Aganagic-Vafa Lagrangian brane. This can be viewed as an all genus open-closed mirror symmetry for affine toric Calabi-Yau 3-orbifolds.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Geometric and Algebraic Topology · Geometry and complex manifolds