Gauge Symmetry Breaking Patterns in an SU(5) Grand Gauge-Higgs Unification

TL;DR

This paper investigates gauge symmetry breaking patterns in a five-dimensional SU(5) grand gauge-Higgs unification model, analyzing matter contents, phase transitions, and vacuum stability, with implications for the standard model and supersymmetry.

Contribution

It identifies matter contents that produce the standard model gauge symmetry and explores vacuum configurations and phase transitions in a 5D SU(5) unification framework.

Findings

Matter contents leading to SU(3)×SU(2)×U(1) symmetry identified

Examples of matter content for various subgroup vacua provided

Standard model vacuum remains stable up to the present in a supersymmetric model

Abstract

We study gauge symmetry breaking patterns of the five-dimensional $SU(5)$ grand gauge-Higgs unification compactified on an orbifold $S^1/{\mathbb Z}_2$ with the Hosotani mechanism in the framework of the diagonal embedding method. We find matter contents that lead to the $SU(3)\times SU(2)\times U(1)$ gauge symmetry on the global minimum of the effective potential and also present examples of matter content for which each regular subgroup of $SU(5)$ is realized as vacuum configuration. The finite temperature phase transitions for the models with the gauge symmetry of the standard model at zero temperature and also for supersymmetric models are studied. We show in a certain model with supersymmetry that the vacuum of the standard model selected dynamically before the inflation continues to stay there up to the present.