Open string instantons and superpotentials

Abstract

We study the F terms in $\mathcal{N}=1$ 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 $({\ensuremath{\alpha}}^{\ensuremath{'}}\ensuremath{\rightarrow}0)$ considerations. If $p=3,$ superpotentials for massless modes are forbidden to all orders in ${\ensuremath{\alpha}}^{\ensuremath{'}}$ 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.