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 threefolds. The domainwall tension is identified with a Poincar´e normal function — 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.