Advances in Theoretical and Mathematical Physics

Volume 20 (2016)

Number 1

The SYZ mirror symmetry and the BKMP remodeling conjecture

Pages: 165 – 192



Bohan Fang (Beijing International Center for Mathematical Research, Peking University, Beijing, China)

Chiu-Chu Melissa Liu (Department of Mathematics, Columbia University, New York, N.Y., U.S.A.)

Zhengyu Zong (Yau Mathematical Sciences Center, Tsinghua University, China)


The Remodeling Conjecture proposed by Bouchard–Klemm–Mariño–Pasquetti (BKMP) relates the A-model open and closed topological string amplitudes (open and closed Gromov–Witten invariants) of a symplectic toric Calabi–Yau 3-fold to Eynard–Orantin invariants of its mirror curve. The Remodeling Conjecture can be viewed as a version of all genus open-closed mirror symmetry. The SYZ conjecture explains mirror symmetry as $T$-duality. After a brief review on SYZ mirror symmetry and mirrors of symplectic toric Calabi–Yau 3-orbifolds, we give a non-technical exposition of our results on the Remodeling Conjecture for symplectic toric Calabi–Yau 3-orbifolds. In the end, we apply SYZ mirror symmetry to obtain the descendent version of the all genus mirror symmetry for toric Calabi–Yau 3-orbifolds.

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