F-Theory GUT Vacua on Compact Calabi-Yau Fourfolds

TL;DR

This paper constructs explicit compact Calabi-Yau fourfolds for F-theory GUT models, demonstrating the feasibility of three-generation models with consistent tadpole cancellation and GUT symmetry breaking.

Contribution

It provides a detailed geometric construction of F-theory GUT vacua on Calabi-Yau fourfolds using toric methods, including explicit flux solutions and decoupling limits.

Findings

Successfully constructed elliptically fibered Calabi-Yau fourfolds with GUT models

Demonstrated D3-tadpole cancellation for three-generation flux solutions

Showed GUT symmetry breaking via hypercharge flux on a del Pezzo surface

Abstract

We present compact three-generation F-theory GUT models meeting in particular the constraints of D3-tadpole cancellation and D-term supersymmetry. To this end we explicitly construct elliptically fibered Calabi-Yau fourfolds as complete intersections in a toric ambient space. Toric methods enable us to control the singular geometry of the SU(5) GUT model. The GUT brane wraps a non-generic del Pezzo surface admitting GUT symmetry breaking via hypercharge flux. It is contractible to a curve and we demonstrate the existence of a consistent decoupling limit. We compute the Euler characteristic of the singular Calabi-Yau fourfold to show that our three-generation flux solutions obtained via the spectral cover construction are consistent with D3-tadpole cancellation.