Gauge coupling unification from unified theories in higher dimensions

Higher dimensional grand unified theories, with gauge symmetry breaking by orbifold compactification, possess $\mathrm{SU}\left(5\right)\mathrm{}$ breaking at fixed points, and do not automatically lead to tree-level gauge coupling unification. A new framework is introduced that guarantees precise unification—even the leading loop threshold corrections are predicted, although they are model dependent. Precise agreement with the experimental result, ${\alpha }_s^{\exp }=0.117\mathrm{}\pm 0.002,$ occurs only for a unique theory, and gives ${\alpha }_s^{\mathrm{KK}}=0.118\mathrm{}\pm 0.004\pm \mathrm{0.003.}$ Remarkably, this unique theory is also the simplest, with $\mathrm{SU}\left(5\right)\mathrm{}$ gauge interactions and two Higgs hypermultiplets propagating in a single extra dimension. This result is more successful and precise than that obtained from conventional supersymmetric grand unification, ${\alpha }_s^{\mathrm{SGUT}}=0.130\mathrm{}\pm 0.004\pm {\Delta }_{\mathrm{SGUT}}.$ There is a simultaneous solution to the three outstanding problems of 4D supersymmetric grand unified theories: a large mass splitting between Higgs doublets and their color triplet partners is forced, proton decay via dimension five operators is automatically forbidden, and the absence of fermion mass relations amongst light quarks and leptons is guaranteed, while preserving the successful $m_b{/m}_{\tau }$ relation. The theory necessarily has a strongly coupled top quark located on a fixed point and part of the lightest generation propagating in the bulk. The string and compactification scales are determined to be around ${10}^{17}\hspace{0.5em}\mathrm{GeV}$ and ${10}^{15}\hspace{0.5em}\mathrm{GeV},$ respectively.