Gauge Unification in Higher Dimensions
Lawrence Hall, Yasunori Nomura
TL;DR
This work develops a complete 5D SU(5) grand unified theory compactified on the orbifold $S^1/(Z_2\times Z_2')$ that naturally yields the MSSM in 4D. Heavy gauge and Higgs states acquire masses through the orbifold projections, achieving automatic doublet-triplet splitting and suppressing dimension-5 proton decay via a bulk $U(1)_R$ symmetry; quarks and leptons reside on SU(5)-preserving branes while Yukawas are generated at fixed points. Gauge coupling unification remains robust with only small brane and KK threshold corrections, and the X-boson mass is tied to the compactification scale $M_c=1/R$, predicting proton decay rates within reach of current experiments. Supersymmetry breaking occurs on a distant brane and is communicated through gaugino mediation, yielding a natural MSSM spectrum with non-unified gaugino masses, while fermion masses and neutrino masses arise from mixing with bulk fields and a seesaw mechanism, providing realistic textures and mass hierarchies.
Abstract
A complete 5-dimensional SU(5) unified theory is constructed which, on compactification on the orbifold with two different Z_2's (Z_2 and Z_2'), yields the minimal supersymmetric standard model. The orbifold accomplishes SU(5) 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(1)_R symmetry. Quarks and leptons and their Yukawa interactions are located at the Z_2 orbifold fixed points, where SU(5) is unbroken. A new mechanism for introducing SU(5) breaking into the quark and lepton masses is introduced, which originates from the SU(5) violation in the zero-mode structure of bulk multiplets. Even though SU(5) is absent at the Z_2' 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 proton decay to e^+ π^0 is expected with a rate within about one order of magnitude of the current limit. Supersymmetry breaking occurs on the Z_2' 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.