中文摘要：

The D-brane superpotential is very important in the low energy effective theory.As the generating function of all disk instantons from the worldsheet point of view,it plays a crucial role in deriving some important properties of the compact Calabi-Yau manifolds.By using the generalized GKZ hypergeometric system,we will calculate the D-brane superpotentials of two non-Fermat type compact Calabi-Yau hypersurfaces in toric varieties,respectively.Then according to the mirror symmetry,we obtain the A-model superpotentials and the Ooguri-Vafa invariants for the mirror Calabi-Yau manifolds.

英文摘要：

The D-brane superpotential is very important in the low energy effective theory. As the generating function of all disk instantons from the worldsheet point of view, it plays a crucial role in deriving some important properties of the compact Calabi Yau manifolds. By using the generalized GKZ hypergeometric system, we will calculate the D-brahe superpotentials of two non-Fermat type compact CMabi Yau hypersurfaces in toric varieties, respectively. Then according to the mirror symmetry, we obtain the A-model superpotentials and the Ooguri Vafa invariants for the mirror Calabi-Yau manifolds.