Instanton superpotentials, Calabi-Yau geometry, and fibrations

In this paper we explore contributions to nonperturbative superpotentials arising from instantons wrapping effective divisors in smooth Calabi-Yau fourfolds. We concentrate on the case of manifolds constructed as complete intersections in products of projective spaces or generalizations thereof. We systematically investigate the structure of the cone of effective (algebraic) divisors in the fourfold geometries and employ the same tools recently developed by Anderson et al. [arXiv:1507.03235] to construct more general instanton geometries than have previously been considered in the literature. We provide examples of instanton configurations on Calabi-Yau manifolds that are elliptically and K3 fibered and explore their consequences in the context of string dualities. The examples discussed include manifolds containing infinite families of divisors with arithmetic genus, χ(D,OD)=1, and superpotentials exhibiting modular symmetry.