Gauge-Higgs unification models in six dimensions with $S^2/Z_2$ extra space and GUT gauge symmetry

TL;DR

This paper reviews six-dimensional gauge-Higgs unification models on an $S^2/Z_2$ space, demonstrating how they can produce Standard Model-like gauge theories with realistic symmetry breaking and particle masses.

Contribution

It compares two construction schemes for gauge-Higgs unification models with GUT gauge symmetry on a non-trivial extra-dimensional space.

Findings

Models achieve Standard Model gauge symmetry with fermions in 4D.

Electroweak symmetry breaking is realized in the models.

Masses for weak gauge bosons and Higgs boson are obtained.

Abstract

In this article, we review gauge-Higgs unification models based on gauge theories defined on six-dimensional spacetime with $S^2/Z_2$ topology in the extra spatial dimensions. On the extra $S^2/Z_2$ space, non-trivial boundary conditions are imposed. This review considers two scenarios for constructing a four-dimensional theory from the six-dimensional model. One scheme utilizes the SO(12) gauge symmetry with a special symmetry condition imposed on the gauge field, whereas the other employs the E$_6$ gauge symmetry without requiring the additional symmetry condition. Both models lead to a Standard Model-like gauge theory with the SU(3) $\times$ SU(2)$_L$ $\times$ U(1)$_Y$($\times$ U(1)$^2$) symmetry and SM fermions in four dimensions. The Higgs sector of the model is also analyzed. The electroweak symmetry breaking can be realized, and the weak gauge boson and Higgs boson masses are obtained.