Advances in Theoretical and Mathematical Physics
Volume 20 (2016)
The SYZ mirror symmetry and the BKMP remodeling conjecture
Pages: 165 – 192
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.