A Minimal S^1/(Z_2 x Z_2') Orbifold GUT

TL;DR

This work embeds an $SU(5)$ GUT in five dimensions on an $S^1/(Z_2 \times Z_2')$ orbifold, using SU(5)-violating boundary conditions to reduce to the MSSM and avoid the doublet-triplet problem by placing the Higgs on the SU(5)-violating brane. It presents two minimal realizations for MSSM matter: on the SU(5)-violating brane (Model I) or in the SU(5) symmetric bulk (Model II), with gauge coupling unification preserved via the bulk symmetry despite brane-induced violations. The running of gauge couplings is analyzed in a 5D effective framework, yielding relationships among the compactification scale $M_c=1/R$, the unification scale $M_{GUT}$, and the strong-coupling onset, with both models producing phenomenologically attractive scenarios. The approach achieves unification and correct fermion quantum numbers without invoking full $SU(5)$ multiplets for MSSM matter in the brane-localized case, while remaining consistent with proton decay constraints.

Abstract

We investigate supersymmetric SU(5) grand-unified theories (GUTs) realized in 5 space-time dimensions and broken down to the MSSM by SU(5)-violating boundary conditions on a S^1/(Z_2 x Z_2') orbifold with two 3-branes. The doublet-triplet splitting problem is entirely avoided by locating the MSSM Higgs doublets on the brane on which SU(5) is not a good symmetry. An extremely simple model is then described in which the MSSM matter is also located on this SU(5)-violating brane. Although this model does not unify the MSSM matter within SU(5) multiplets, it explains gauge coupling unification. A second model with MSSM matter in the SU(5)-symmetric bulk preserves both the SU(5) explanation of fermion quantum numbers as well as gauge-coupling unification. Both models naturally avoid problematic SU(5) predictions for the Yukawa couplings of the first two generations and are consistent with proton decay constraints. We analyse the running of gauge couplings above the compactification scale in terms of a 5d effective action and derive the implications for the values of compactification scale, unification scale and of the scale at which the bulk gauge theory becomes strongly coupled.