On Instanton Superpotentials, Calabi-Yau Geometry, and Fibrations

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.

27 pages. v2: a footnote and references added, a paragraph inserted in the introduction and wordings adjusted to more clearly state our focus

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• Orientifold Calabi-Yau Threefolds with Divisor Involutions and String Landscape
• Superpotentials from Singular Divisors
• A remark on generalized complete intersections
• $E_6$ Yukawa couplings in F-theory as D-brane instanton effects
• Non-vanishing Heterotic Superpotentials on Elliptic Fibrations
• Generalized Vanishing Theorems for Yukawa Couplings in Heterotic Compactifications
• Numerical spectra of the Laplacian for line bundles on Calabi-Yau hypersurfaces
• Line Bundle Hidden Sectors for Strongly Coupled Heterotic Standard Models
• Eigenvalues and eigenforms on Calabi-Yau threefolds
• Heterotic Line Bundle Models on Generalized Complete Intersection Calabi Yau Manifolds
• Machine Learning on generalized Complete Intersection Calabi-Yau Manifolds
• Calabi-Yau generalized complete intersections and aspects of cohomology of sheaves
• New Evidence for (0,2) Target Space Duality