SO(10) and SU(6) Unified Theories on an Elongated Rectangle

Maximally supersymmetric SO(10) and SU(6) unified theories are constructed on the orbifold T^2/(Z_2 x Z'_2), with one length scale R_5 taken much larger than the other, R_6. The effective theory below 1/R_6 is found to be the highly successful SU(5) theory in 5D with natural doublet-triplet splitting, no proton decay from operators of dimension four or five, unified mass relations for heavier generations only, and a precise prediction for gauge coupling unification. A more unified gauge symmetry, and the possibility of Higgs doublets being components of the higher dimensional gauge multiplet, are therefore compatible with a large energy interval where physics is described by SU(5) gauge symmetry in 5D. This leads to the distinctive branching ratios for proton decay from SU(5) gauge boson exchange, p -> l^+ pi^0, l^+ K^0, \bar{nu} pi^+, \bar{nu} K^+ (l = e, mu), for well-motivated locations for matter. Several phenomenological features of the higher unified gauge symmetry are discussed, including the role of an extra U(1) gauge symmetry, which survives compactification, in the generation of neutrino masses.