Open mirror symmetry for Pfaffian Calabi-Yau 3-folds

We investigate the open mirror symmetry of certain non-complete intersection Calabi- Yau 3-folds, so called pfaffian Calabi-Yau. We perform the prediction of the number of disk invariants of several examples by using the direct integration method proposed recently and the open mirror symmetry. We treat several pfaffian Calabi-Yau 3-folds in $\mathbb{P}^6$ and branes with two discrete vacua. Some models have the two special points in its moduli space, around both of which we can consider different A-model mirror partners. We compute disc invariants for both cases. This study is the first application of the open mirror symmetry to the compact non-complete intersections in toric variety.