Moduli Webs and Superpotentials for Five-Branes

Uses matrix factorisations of Landau–Ginzburg models to study D5-branes wrapping lines in one-parameter Calabi–Yau manifolds such as the quintic, whose moduli spaces form webs of curves meeting at permutation branes. This yields open–closed superpotentials to all orders and shows which branes survive bulk deformations.

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.

Recommended citation: M. Baumgartl and S. Wood, JHEP 06, 052 (2009)
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