Effective superpotentials for compact D5-brane Calabi-Yau geometries

TL;DR

This paper develops methods to compute effective superpotentials for compact Calabi-Yau geometries with D5-branes, linking open/closed string deformations to physical quantities like domain wall tensions and Gromov-Witten invariants.

Contribution

It introduces techniques to derive and solve open/closed Picard-Fuchs equations for D5-brane Calabi-Yau geometries, enabling explicit superpotential calculations.

Findings

Derived open/closed Picard-Fuchs equations for D5-brane geometries

Expressed superpotentials in flat coordinates for explicit examples

Reproduced domain wall tensions and extracted orbifold disk invariants

Abstract

For compact Calabi-Yau geometries with D5-branes we study N=1 effective superpotentials depending on both open- and closed-string fields. We develop methods to derive the open/closed Picard-Fuchs differential equations, which control D5-brane deformations as well as complex structure deformations of the compact Calabi-Yau space. Their solutions encode the flat open/closed coordinates and the effective superpotential. For two explicit examples of compact D5-brane Calabi-Yau hypersurface geometries we apply our techniques and express the calculated superpotentials in terms of flat open/closed coordinates. By evaluating these superpotentials at their critical points we reproduce the domain wall tensions that have recently appeared in the literature. Finally we extract orbifold disk invariants from the superpotentials, which, up to overall numerical normalizations, correspond to orbifold disk Gromov-Witten invariants in the mirror geometry.