Toric Construction of Global F-Theory GUTs

TL;DR

This paper systematically constructs a large class of elliptically fibered Calabi-Yau fourfolds suitable for F-theory GUTs, providing a comprehensive database and analyzing geometric constraints for model building.

Contribution

It introduces a method to construct and classify Calabi-Yau fourfolds for F-theory GUTs using toric geometry, significantly narrowing down viable models.

Findings

Strong geometric constraints reduce model space

Database of models is publicly available

Several detailed examples are provided

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.