On the Remodeling Conjecture for Toric Calabi-Yau 3-Orbifolds

Abstract

The Remodeling Conjecture proposed by Bouchard-Klemm-Mariño-Pasquetti (BKMP) [arXiv:0709.1453, arXiv:0807.0597] relates the A-model open and closed topological string amplitudes (the all genus open and closed Gromov-Witten invariants) of a semi-projective toric Calabi-Yau 3-manifold/3-orbifold to the Eynard-Orantin invariants of its mirror curve. It is an all genus open-closed mirror symmetry for toric Calabi-Yau 3-manifolds/3-orbifolds. In this paper, we present a proof of the BKMP Remodeling Conjecture for all genus open-closed orbifold Gromov-Witten invariants of an arbitrary semi-projective toric Calabi-Yau 3-orbifold relative to an outer framed Aganagic-Vafa Lagrangian brane. We also prove the conjecture in the closed string sector at all genera.

85 pages, 4 figures; final version

References in corpus (12)

• Open string amplitudes and large order behavior in topological string theory
• Holomorphic anomaly and matrix models
• Local Mirror Symmetry for One-Legged Topological Vertex
• Quantum Cohomology and Crepant Resolutions: A Conjecture
• Quantization of open-closed BCOV theory, I
• Bouchard-Klemm-Marino-Pasquetti Conjecture for ${\mathbb{C}}^3$
• A mirror theorem for genus two Gromov-Witten invariants of quintic threefolds
• Local Mirror Symmetry for the Topological Vertex
• Topological Strings and (Almost) Modular Forms
• Seidel Representations and Quantum Cohomology of Toric Orbifolds
• On the Connectedness of Moduli Spaces of Flat Connections over Compact Surfaces
• Genus one GW invariants of quintic threefolds via MSP localization

Cited by in corpus (15)

• Stable maps to Looijenga pairs
• Integrality structures in topological strings I: framed unknot
• Topological Recursion in The Ramond Sector
• Gromov-Witten Invariants of Local P^2 and Modular Forms
• Hodge-GUE correspondence and the discrete KdV equation
• Matrix models for topological strings: exact results in the planar limit
• Stable quotients and the holomorphic anomaly equation
• Topological strings, quiver varieties and Rogers-Ramanujan identities
• Reconstructing GKZ via topological recursion
• The SYZ mirror symmetry and the BKMP remodeling conjecture
• $T$-equivariant disc potentials for toric Calabi-Yau manifolds
• $\mathcal{N}=1$ Super Topological Recursion
• Topological recursion for the conifold transition of a torus knot
• Les Houches lecture notes on moduli spaces of Riemann surfaces
• Integration on complex Grassmannians, deformed monotone Hurwitz numbers, and interlacing phenomena