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On the remodeling conjecture for toric Calabi-Yau 3-orbifolds


Authors: Bohan Fang, Chiu-Chu Melissa Liu and Zhengyu Zong
Journal: J. Amer. Math. Soc. 33 (2020), 135-222
MSC (2010): Primary 14N35, 15D35, 14J33
DOI: https://doi.org/10.1090/jams/934
Published electronically: November 1, 2019
MathSciNet review: 4066474
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Abstract: The Remodeling Conjecture proposed by Bouchard-Klemm-Mariño-Pasquetti (BKMP) relates the A-model open and closed topological string amplitudes (the all genus open and closed Gromov-Witten invariants) of a semiprojective 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 semiprojective 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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Additional Information

Bohan Fang
Affiliation: Beijing International Center for Mathematical Research, Peking University, 5 Yiheyuan Road, Beijing 100871, People’s Republic of China
MR Author ID: 831818
Email: bohanfang@gmail.com

Chiu-Chu Melissa Liu
Affiliation: Department of Mathematics, Columbia University, 2990 Broadway, New York, New York 10027
MR Author ID: 691648
Email: ccliu@math.columbia.edu

Zhengyu Zong
Affiliation: Yau Mathematical Sciences Center, Tsinghua University, Jin Chun Yuan West Building, Tsinghua University, Haidian District, Beijing 100084, People’s Republic of China
MR Author ID: 1056175
Email: zyzong@mail.tsinghua.edu.cn

Received by editor(s): March 31, 2018
Received by editor(s) in revised form: June 20, 2019
Published electronically: November 1, 2019
Additional Notes: The first author was partially supported by a start-up grant at Peking University
The second author was partially supported by NSF grants DMS-1206667 and DMS-1159416
The third author was partially supported by the start-up grant at Tsinghua University
Article copyright: © Copyright 2019 American Mathematical Society