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

TL;DR

This paper proves the BKMP Remodeling Conjecture, establishing a deep connection between open-closed Gromov-Witten invariants of toric Calabi-Yau 3-orbifolds and Eynard-Orantin invariants of their mirror curves across all genera.

Contribution

It provides a comprehensive proof of the BKMP Remodeling Conjecture for all genus open-closed orbifold Gromov-Witten invariants of semi-projective toric Calabi-Yau 3-orbifolds, including the closed string sector.

Findings

Proof of the BKMP Remodeling Conjecture for open-closed orbifold Gromov-Witten invariants.

Verification of the conjecture in the closed string sector at all genera.

Establishment of all genus open-closed mirror symmetry for toric Calabi-Yau 3-orbifolds.

Abstract

The Remodeling Conjecture proposed by Bouchard-Klemm-Mari\~{n}o-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.