On Instanton Superpotentials, Calabi-Yau Geometry, and Fibrations

TL;DR

This paper investigates non-perturbative superpotentials from instantons on Calabi-Yau four-folds, focusing on divisor structures, novel instanton geometries, and implications for string dualities, including modular symmetry phenomena.

Contribution

It systematically analyzes divisor cones and constructs new instanton geometries on Calabi-Yau four-folds, extending previous work with explicit examples and duality insights.

Findings

Identified infinite families of divisors with arithmetic genus one.

Constructed new instanton configurations on elliptically and K3-fibered Calabi-Yau manifolds.

Discovered superpotentials with modular symmetry properties.

Abstract

In this paper we explore contributions to non-perturbative superpotentials arising from instantons wrapping effective divisors in smooth Calabi-Yau four-folds. We concentrate on the case of manifolds constructed as complete intersections in products of projective spaces (CICYs) or generalizations thereof (gCICYs). We systematically investigate the structure of the cone of effective (algebraic) divisors in the four-fold geometries and employ the same tools recently developed in 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, $\chi(D, \mathcal O_D)=1$ and superpotentials exhibiting modular symmetry.