A Note on Computations of D-brane Superpotential

TL;DR

This paper introduces computational techniques for evaluating 3-chain integrals on Calabi-Yau 3-folds, crucial for understanding open mirror symmetry in topological B-models, through systematic algorithms and analytic continuation methods.

Contribution

It presents new algorithms for deriving inhomogeneous Picard-Fuchs equations and a direct integration approach for 3-chain integrals, enhancing computational tools in open mirror symmetry.

Findings

Developed a systematic algorithm for inhomogeneous Picard-Fuchs equations.

Established a direct analytic continuation method for 3-chain integrals.

Applicable to both on-shell and off-shell formalisms in topological B-models.

Abstract

We develop some computational methods for the integrals over the 3-chains on the compact Calabi-Yau 3-folds that plays a prominent role in the analysis of the topological B-model in the context of the open mirror symmetry. We discuss such 3-chain integrals in two approaches. In the first approach, we provide a systematic algorithm to obtain the inhomogeneous Picard-Fuchs equations. In the second approach, we discuss the analytic continuation of the period integral to compute the 3-chain integral directly. The latter direct integration method is applicable for both on-shell and off-shell formalisms.