Flipped SU(5) X U(1)_X Models from F-Theory

TL;DR

This work addresses gauge coupling unification in flipped SU(5) × U(1)_X models derived from F-theory by introducing vector-like multiplets to realize a decoupling scenario between the GUT and string scales. It systematically builds models with and without bulk vector-like particles, analyzes one- and two-loop renormalization group evolution and flux contributions, and computes the unification scales $M_{23}$ and $M_U$ across multiple types (I–III) and threshold configurations. The key findings show that at most five TeV-scale vector-like sets can be accommodated without Landau poles, that $U(1)_X$ flux contributions preserve unification, and that several TeV-scale scenarios yield testable predictions for the LHC and Hyper-Kamiokande, including proton decay rates, Higgs-mass enhancements, and cosmological implications. The results provide a versatile framework for constructing realistic F-theory GUTs with potentially observable signatures.

Abstract

We systematically construct flipped SU(5) X U(1)_X models without and with bulk vector-like particles from F-theory. To realize the decoupling scenario, we introduce sets of vector-like particles in complete SU(5) X U(1) multiplets at the TeV scale, or at the intermediate scale, or at the TeV scale and high scale. To avoid the Landau pole problem for the gauge couplings, we can only introduce five sets of vector-like particles around the TeV scale. These vector-like particles can couple to the Standard Model singlet fields, and obtain suitable masses by Higgs mechanism. We study gauge coupling unification in detail. We show that the U(1)_X flux contributions to the gauge couplings preserve the SU(5) X U(1)_X gauge coupling unification. We calculate the SU(3)_C X SU(2)_L unification scales, and the SU(5) X U(1)_X unification scales and unified couplings. In most of our models, the high-scale or bulk vector-like particles can be considered as string-scale threshold corrections since their masses are close to the string scale. Futhermore, we discuss the phenomenological consequences of our models. In particular, in the models with TeV-scale vector-like particles, the vector-like particles can be observed at the Large Hadron collider, the proton decay is within the reach of the future Hyper-Kamiokande experiment, the lightest CP-even Higgs boson mass can be increased, the hybrid inflation can be naturally realized, and the correct cosmic primodial density fluctuations can be generated.

Figures (4)

• Figure 1: Gauge coupling unification in the Type IA model with $M_V=1 ~{\rm TeV}$ and $M_S=800 ~{\rm GeV}$ (left figure), and in the Type IB model with $M_V=20 ~{\rm TeV}$ and $M_S=800 ~{\rm GeV}$.
• Figure 2: String-scale gauge coupling unification in the Type IIA model (left figure) and Type IIB model (right figure) with $M_S=800 ~{\rm GeV}$.
• Figure 3: String-scale gauge coupling unification in the Type IIIB1 model (left figure) and Type IIIB2 model (right figure) with $M_V=1 ~{\rm TeV}$ and $M_S=800 ~{\rm GeV}$.
• Figure 4: The string-scale gauge coupling unification in the Type IIA1 model with $M_V=800~{\rm GeV}$ and $M_S=800 ~{\rm GeV}$ (left figure) and in the Type IIA2 model with $M_V=1 ~{\rm TeV}$ and $M_S=800 ~{\rm GeV}$ (right figure).