Kwokwai Chan, Cheol-Hyun Cho, Siu-Cheong Lau, Hsian-Hua Tseng
We investigate the relationship between the Lagrangian Floer superpotentials for a toric orbifold and its toric crepant resolutions. More specifically, we study an open string version of the crepant resolution conjecture (CRC) which states that the Lagrangian Floer superpotential of a Gorenstein toric orbifold $\mathcal{X}$ and that of its toric crepant resolution $Y$ coincide after analytic continuation of quantum parameters and a change of variables. Relating this conjecture with the closed CRC, we discover a geometric explanation (in terms of virtual counting of stable orbi-discs) for the specialization of quantum parameters to roots of unity which appeared in Y. Ruan's original CRC. We prove the open CRC for the weighted projective spaces $\mathcal{X}=\proj(1,...,1,n)$ using an equality between open and closed orbifold Gromov-Witten invariants. Along the way, we also prove an open mirror theorem for these toric orbifolds.
View original:
http://arxiv.org/abs/1208.5282
No comments:
Post a Comment