D-branes and normal functions

Abstract

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