Moduli Webs and Superpotentials for Five-Branes

TL;DR

This paper explores the geometry of D5-brane moduli spaces in Calabi-Yau models, revealing a web structure of Riemann curves and computing superpotentials that encode open-closed string interactions.

Contribution

It introduces a geometric framework for understanding D5-brane moduli and calculates effective superpotentials to all orders in open string couplings.

Findings

Identification of D5-brane families associated with embedded lines

Description of moduli spaces as webs of Riemann curves

Computation of open-closed superpotentials to all orders

Abstract

We investigate the one-parameter Calabi-Yau models and identify families of D5-branes which are associated to lines embedded in these manifolds. The moduli spaces are given by sets of Riemann curves, which form a web whose intersection points are described by permutation branes. We arrive at a geometric interpretation for bulk-boundary correlators as holomorphic differentials on the moduli space and use this to compute effective open-closed superpotentials to all orders in the open string couplings. The fixed points of D5-brane moduli under bulk deformations are determined.