Open string instantons and superpotentials

TL;DR

This paper investigates the generation of superpotentials in N=1 supersymmetric gauge theories from D-branes on Calabi-Yau manifolds, highlighting the role of open string instantons especially for p=3 cases.

Contribution

It demonstrates that superpotentials for p=3 branes are generated by open string instantons, and explores mirror symmetry relating perturbative and nonperturbative effects.

Findings

Superpotentials for p=3 branes are generated by open string instantons.

Classical considerations determine superpotentials for even p branes.

Mirror symmetry relates superpotentials for even and odd p cases.

Abstract

We study the F-terms in N=1 supersymmetric, d=4 gauge theories arising from D(p+3)-branes wrapping supersymmetric p-cycles in a Calabi-Yau threefold. If p is even the spectrum and superpotential for a single brane are determined by purely classical ($\alpha^\prime \to 0$) considerations. If p=3, superpotentials for massless modes are forbidden to all orders in $\alpha^\prime$ and may only be generated by open string instantons. For this latter case we find that such instanton effects are generically present. Mirror symmetry relates even and odd p and thus perturbative and nonperturbative superpotentials; we provide a preliminary discussion of a class of examples of such mirror pairs.