D-branes and Normal Functions

TL;DR

This paper explores the B-model origin of extended Picard-Fuchs equations related to D-brane superpotentials on Calabi-Yau threefolds, linking domainwall tension to normal functions via the Abel-Jacobi map.

Contribution

It introduces a formalism connecting D-brane superpotentials with normal functions and derives the extended Picard-Fuchs equation for the mirror of the real quintic.

Findings

Identification of domainwall tension with a Poincare normal function

Derivation of extended Picard-Fuchs equations for specific Calabi-Yau examples

Formalism linking D-brane superpotentials to Griffiths intermediate Jacobian

Abstract

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.