All Genus Open-Closed Mirror Symmetry for Affine Toric Calabi-Yau 3-Orbifolds

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.

49 pages, 2 figures; final version

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Cited by in corpus (16)

• Quantum curves for Hitchin fibrations and the Eynard-Orantin theory
• A short overview of the "Topological recursion"
• The Eynard-Orantin recursion and equivariant mirror symmetry for the projective line
• On the Remodeling Conjecture for Toric Calabi-Yau 3-Orbifolds
• Quantum curves and conformal field theory
• Topological recursion and a quantum curve for monotone Hurwitz numbers
• Super Quantum Airy Structures
• Matrix models for topological strings: exact results in the planar limit
• Reconstructing GKZ via topological recursion
• The SYZ mirror symmetry and the BKMP remodeling conjecture
• $q$-Difference Kac-Schwarz Operators in Topological String Theory
• Frobenius Manifolds, Spectral Curves, and Integrable Hierarchies
• Counting curves on surfaces
• Topological recursion, topological quantum field theory and Gromov-Witten invariants of BG
• Equivariant Gromov-Witten Theory of Affine Smooth Toric Deligne-Mumford Stacks
• Gromov-Witten invariants of ${\mathrm{Sym}}^d{\mathbb{P}}^r$