Off-shell superpotentials and Ooguri-Vafa invariants of type Ⅱ/F theory compactification

In this paper, we calculate the off-shell superpotential of two Calabi-Yau manifolds with three parameters by integrating the period of the subsystem. We also obtain the Ooguri-Vafa invariants with open mirror symmetry.     

D-brane superpotentials and Ooguri-Vafa invariants of compact Calabi-Yau threefolds

We calculate the D-brane superpotentials for two compact Calabi-Yau manifolds X14(1,1,2,3,7) and X8(1, 1, 1, 2, 3) which are of non-Fermat type in the type II string theory. By constructing the open mirror symmetry,we also compute the Ooguri-Vafa invariants, which are related to the open Gromov-Witten invariants.     

Another representation of the β form of the inhomogeneous Picard-Fuchs equation

In this letter we give another representation of the β form in the inhomogeneous Picard-Fuchs equation for open topological string for some one-parameter Calabi-Yau hypersurfaces in weighted projective spaces. Furthermore, the corresponding domain wall tensions calculated by using these β forms are consistent with the results that appear in literature. The β form is essential for the calculation of the D-brane domain wall tension, and a convenient choice of β forms should simplify the calculation. The freedom of the choice of β forms shows some symmetries in Calabi-Yau space.