Superpotentials of D-branes in Calabi-Yau manifolds with several moduli by mirror symmetry and blown-up

Abstract

We study B-brane superpotentials depending on several closed- and open-moduli on Calabi-Yau hypersurfaces and complete intersections. By blowing up the ambient space along a curve wrapped by B-branes in a Calabi-Yau manifold, we obtain a blow-up new manifold and the period integral satisfying the GKZ-system. Via mirror symmetry to A-model, we calculate the superpotentials and extract Ooguri-Vafa invariants for concrete examples of several open-closed moduli in Calabi-Yau manifolds.