Gauge unification in higher dimensions

A complete 5-dimensional $\mathrm{SU}\left(5\right)\mathrm{}$ unified theory is constructed which, on compactification on the orbifold with two different $Z_2$’s ${(Z}_2$ and $Z_2^{\prime }),$ yields the minimal supersymmetric standard model. The orbifold accomplishes $\mathrm{SU}\left(5\right)\mathrm{}$ gauge symmetry breaking, doublet-triplet splitting, and a vanishing of proton decay from operators of dimension 5. Until 4D supersymmetry is broken, all proton decay from dimension 4 and dimension 5 operators is forced to vanish by an exact ${U\left(1\right)\mathrm{}}_R$ symmetry. Quarks and leptons and their Yukawa interactions are located at the $Z_2$ orbifold fixed points, where $\mathrm{SU}\left(5\right)\mathrm{}$ is unbroken. A new mechanism for introducing $\mathrm{SU}\left(5\right)\mathrm{}$ breaking into the quark and lepton masses is introduced, which originates from the $\mathrm{SU}\left(5\right)\mathrm{}$ violation in the zero-mode structure of bulk multiplets. Even though $\mathrm{SU}\left(5\right)\mathrm{}$ is absent at the $Z_2^{\prime }$ orbifold fixed point, the brane threshold corrections to gauge coupling unification are argued to be negligibly small, while the logarithmic corrections are small and in a direction which improves the agreement with the experimental measurements of the gauge couplings. Furthermore, the X gauge boson mass is lowered, so that $\overrightarrow{p}{e}^{+}{\pi }^0$ is expected with a rate within about one order of magnitude of the current limit. Supersymmetry breaking occurs on the $Z_2^{\prime }$ orbifold fixed point, and is felt directly by the gauge and Higgs sectors, while squarks and sleptons acquire mass via gaugino mediation, solving the supersymmetric flavor problem.