Toric Construction of Global F-Theory GUTs

TL;DR

<3-5 sentence high-level summary> The paper develops a systematic, toric-based pipeline to construct and analyze global F-theory GUTs by generating a vast catalogue of elliptically fibered Calabi–Yau fourfolds built over base manifolds that are hypersurfaces in toric ambient spaces. It imposes Tate model factorization for SU(5) and SO(10) GUTs, identifies del Pezzo divisors as GUT branes, and computes matter curves, Yukawa points, and decoupling limits, using nef partitions and reflexive polytopes to ensure global consistency. It reveals strong geometric constraints that dramatically reduce viable models, assembles a large database, and demonstrates both successes and subtleties through detailed examples, including cases where Euler numbers deviate from simple global formulas due to extra enhancements. The work provides a valuable global-geometry resource for connecting local F-theory GUT models to explicit string compactifications and sets the stage for future flux, chirality, and symmetry studies within a broad toric framework.

Abstract

We systematically construct a large number of compact Calabi-Yau fourfolds which are suitable for F-theory model building. These elliptically fibered Calabi-Yaus are complete intersections of two hypersurfaces in a six dimensional ambient space. We first construct three-dimensional base manifolds that are hypersurfaces in a toric ambient space. We search for divisors which can support an F-theory GUT. The fourfolds are obtained as elliptic fibrations over these base manifolds. We find that elementary conditions which are motivated by F-theory GUTs lead to strong constraints on the geometry, which significantly reduce the number of suitable models. The complete database of models is available at http://hep.itp.tuwien.ac.at/f-theory/. We work out several examples in more detail.