Relative periods and open-string integer invariants for a compact Calabi-Yau hypersurface

TL;DR

This paper computes relative periods for B-branes on a compact Calabi-Yau hypersurface using direct integration, enabling the extraction of disk instanton invariants and superpotentials relevant for mirror symmetry and string theory.

Contribution

It introduces a generalizable method for calculating relative periods and integer invariants for B-branes in compact Calabi-Yau hypersurfaces, advancing computational techniques in mirror symmetry.

Findings

Derived relative periods for B-branes in a specific Calabi-Yau geometry.

Extracted disk instanton generated superpotentials.

Obtained integer invariants from the superpotentials.

Abstract

In this work we compute relative periods for B-branes, realized in terms of divisors in a compact Calabi-Yau hypersurface, by means of direct integration. Although we exemplify the method of direct integration with a particular Calabi-Yau geometry, the recipe automatically generalizes for divisors in other Calabi-Yau geometries as well. From the calculated relative periods we extract double-logarithmic periods. These periods qualify to describe disk instanton generated N=1 superpotentials of the corresponding compact mirror Calabi-Yau geometry in the large volume regime. Finally we extract the integer invariants encoded in these brane superpotentials.