Mirror-family conjecture for the Pfaffian and Grassmannian Calabi–Yau sections

Let $M_y$ and $W_y$ be the two parts of the B-model moduli space, and let $X_A$ and $Y_A$ be the corresponding two parts of the A-model (Kähler) moduli space. Write $M_y+W_y$ and $X_A+Y_A$ for the resulting pairs of families.

Mirror-family conjecture. The pair $M_y+W_y$ is the mirror family of $X_A+Y_A$, with $M_y$ and $W_y$ forming different parts of the B-model moduli space and $X_A$ and $Y_A$ forming different parts of the A-model (Kähler) moduli space.

This conjecture expresses the proposed mirror-symmetry relation between the Pfaffian and Grassmannian Calabi–Yau sections. The paper establishes that the B-models of $M_y$ and $W_y$ have the same Picard–Fuchs operator and conjectures that their Yukawa couplings agree, but the full mirror-family identification is not established there.