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arXiv · 1604.07123

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

Bohan Fang·Chiu-Chu Melissa Liu·Zhengyu Zong
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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.

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Bohan Fang, Chiu-Chu Melissa Liu, Zhengyu Zong. 2016-04-25. On the Remodeling Conjecture for Toric Calabi-Yau 3-Orbifolds. https://arxiv.org/abs/1604.07123

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