Models with rank-reducing discrete boundary conditions on $T^2/{\mathbb Z}_4$

TL;DR

This paper explores six-dimensional $SU(n)$ gauge models on an orbifold with rank-reducing boundary conditions, proposing a minimal $SU(6)$ model where two Higgs doublets emerge naturally and electroweak symmetry breaking occurs via the Hosotani mechanism.

Contribution

It introduces a minimal $SU(6)$ gauge model with discrete boundary conditions that naturally unifies quarks and Higgs fields without exotic particles, and demonstrates the stability of the Higgs mass against quadratic divergences.

Findings

A minimal $SU(6)$ model describes electroweak symmetry breaking.

Two Higgs doublets originate from extra-dimensional gauge fields.

Quadratic divergences are not reintroduced at higher orders.

Abstract

We study six-dimensional $SU(n)$ gauge models with rank-reducing discrete boundary conditions on the orbifold $T^2/{\mathbb Z}_4$, without and with continuous Wilson line phases. For the latter case, we find that a minimal model can describe the breakdown of the electroweak symmetry based on an $SU(6)$ gauge group. This model possesses excellent features that two Higgs doublets come from the zero modes of the extra-dimensional gauge field, and the quarks in each generation can be unified into one multiplet, without exotic quarks, as the zero modes of a bulk field in the $\boldsymbol{15}$ representation of $SU(6)$. There exists a vacuum where the electroweak symmetry is slightly broken by the Hosotani mechanism, with the addition of suitable bulk fields. %adding suitable bulk fields, and Interestingly, quadratic divergences are not reintroduced into the Higgs masses from the tadpole terms of the field strength localized on fixed points, not only at one-loop level but also at higher orders.