Grand Unification in the Projective Plane

A 6-dimensional grand unified theory with the compact space having thetopology of a real projective plane, i.e., a 2-sphere with opposite pointsidentified, is considered. The space is locally flat except for two conicalsingularities where the curvature is concentrated. One supersymmetry ispreserved in the effective 4d theory. The unified gauge symmetry, for exampleSU(5), is broken only by the non-trivial global topology. In contrast to theHosotani mechanism, no adjoint Wilson-line modulus associated with thisbreaking appears. Since, locally, SU(5) remains a good symmetry everywhere, noUV-sensitive threshold corrections arise and SU(5)-violating local operatorsare forbidden. Doublet-triplet splitting can be addressed in the context of a6d N=2 super Yang-Mills theory with gauge group SU(6). If this symmetry isfirst broken to SU(5) at a fixed point and then further reduced to the standardmodel group in the above non-local way, the two light Higgs doublets of theMSSM are predicted by the group-theoretical and geometrical structure of themodel.Comment: 10 pages LaTeX, 2 figure