D-branes and Normal Functions

We explain the B-model origin of extended Picard-Fuchs equations satisfied by the D-brane superpotential on compact Calabi-Yau threefolds. Via the Abel-Jacobi map, the domainwall tension is identified with a Poincare normal function–a transversal holomorphic section of the Griffiths intermediate Jacobian. Within this formalism, we derive the extended Picard-Fuchs equation associated with the mirror of the real quintic.