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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关于复曲面Calabi-Yau 3-orbifolds的重构猜想

Bouchard-Klemm-Mari\~{n}o-Pasquetti (BKMP) [arXiv:0709.1453, arXiv:0807.0597] 提出的重构猜想将 A 模型开和闭拓扑弦振幅（所有属开和闭 Gromov-半射影复曲面 Calabi-Yau 3-流形/3-轨道的 Witten 不变量到其镜像曲线的 Eynard-Orantin 不变量。它是复曲面 Calabi-Yau 3-流形/3-轨道的全属开闭镜像对称。在本文中，我们针对相对于外框 Aganagic-Vafa Lagrangian 膜的任意半射影复曲面 Calabi-Yau 3-orbifold 的所有属开闭orbifold Gromov-Witten 不变量提出了 BKMP 重构猜想的证明。我们还在所有属的闭弦扇区中证明了猜想。