Advances in Theoretical and Mathematical Physics

Volume 20 (2016)

Number 1

The SYZ mirror symmetry and the BKMP remodeling conjecture

Pages: 165 – 192

DOI: http://dx.doi.org/10.4310/ATMP.2016.v20.n1.a3

Authors

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)

Abstract

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.

Full Text (PDF format)