Gauge Symmetry Reduction from the Extra Space $S^1/Z_2$

TL;DR

The work investigates symmetry reduction arising from compactifying a 5D theory on the orbifold $S^1/Z_2$, showing that a non-universal $Z_2$ parity across multiplet components can erase full multiplets and reduce the 4D symmetry. It develops a framework, and applies it to a 5D $SU(5)$ GUT with bulk gauge and Higgs fields and SM matter on a wall, achieving $G_{SM}$ in 4D and realizing triplet–doublet splitting via boundary conditions. The model yields tree-level gauge-coupling unification $g_3=g_2=g_1=g_U$ and Yukawa relations $f_d=f_e=f_D$, while avoiding tree-level couplings of quarks/leptons to certain heavy gauge or scalar states. However, it faces several challenges, including light exotic states that could induce proton decay, the gauge hierarchy problem, and questions about radiative stability and parity selection, motivating further refinements and localization schemes.

Abstract

We study a mechanism of symmetry transition upon compactification of a 5-dimensional field theory on $S^1/Z_2$. The transition occurs unless all components in a multiplet of a symmetry group have a common $Z_2$ parity on $S^1/Z_2$. This mechanism is applied to a reduction of SU(5) gauge symmetry in grand unified theory, and phenomenological implications are discussed.