Towards Open String Mirror Symmetry for One-Parameter Calabi-Yau Hypersurfaces

TL;DR

This paper investigates the mathematical structure of branes in one-parameter Calabi-Yau hypersurfaces, deriving differential equations for brane superpotentials and predicting BPS invariants relevant to mirror symmetry.

Contribution

It introduces inhomogeneous Picard--Fuchs equations for specific B-branes in Calabi-Yau hypersurfaces, advancing the understanding of open string mirror symmetry.

Findings

Derived inhomogeneous Picard--Fuchs equations for brane superpotentials

Predicted real BPS invariants for low Euler characteristic maps

Established connections between brane geometry and mirror symmetry

Abstract

This work is concerned with branes and differential equations for one-parameter 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.