# The Standard Model Gauge Symmetry from Higher-Rank Unified Groups in Grand Gauge-Higgs Unification Models

## TL;DR

This paper explores grand unified theories in five dimensions with orbifold compactification, demonstrating how gauge symmetry breaking via vacuum expectation values leads to the standard model gauge group, with detailed effective potential calculations.

## Contribution

It introduces specific higher-rank unified models in five dimensions and analyzes their symmetry breaking patterns using one-loop effective potentials.

## Key findings

- Residual gauge symmetry can be broken to the standard model gauge group.
- Effective potentials depend on bulk fermion content.
- Models with SU(7), SU(8), SO(10), and E6 are viable.

## Abstract

We study grand unified models in the five-dimensional space-time where the extra dimension is compactified on $S^1/Z_2$. The spontaneous breaking of unified gauge symmetries is achieved via vacuum expectation values of the extra-dimensional components of gauge fields. We derive one-loop effective potentials for the zero modes of the gauge fields in SU(7), SU(8), SO(10), and $E_6$ models. In each model, the rank of the residual gauge symmetry that respects the boundary condition imposed at the orbifold fixed points is higher than that of the standard model. We verify that the residual symmetry is broken to the standard model gauge symmetry at the global minima of the effective potential for certain sets of bulk fermion fields in each model.