English

The SYZ mirror symmetry and the BKMP remodeling conjecture

Algebraic Geometry 2017-06-06 v1

Abstract

The Remodeling Conjecture proposed by Bouchard-Klemm-Mari\~{n}o-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 TT-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.

Keywords

Cite

@article{arxiv.1607.06935,
  title  = {The SYZ mirror symmetry and the BKMP remodeling conjecture},
  author = {Bohan Fang and Chiu-Chu Melissa Liu and Zhengyu Zong},
  journal= {arXiv preprint arXiv:1607.06935},
  year   = {2017}
}

Comments

18 pages. Exposition of arXiv:1604.07123