Towards open string mirror symmetry for one-parameter Calabi–Yau hypersurfaces

Abstract

This work is concerned with branes and differential equations for oneparameter Calabi–Yau hypersurfaces in weighted projective spaces. For a certain class of B-branes, we derive the inhomogeneous Picard–Fuchs equations satisfied by the brane superpotential. In this way, we arrive at a prediction for the real BPS invariants for holomorphic maps of worldsheets with low Euler characteristics, ending on the mirror A-branes.