  A 6-dimensional grand unified theory with the compact space having the
topology of a real projective plane, i.e., a 2-sphere with opposite points
identified, is considered. The space is locally flat except for two conical
singularities where the curvature is concentrated. One supersymmetry is
preserved in the effective 4d theory. The unified gauge symmetry, for example
SU(5), is broken only by the non-trivial global topology. In contrast to the
Hosotani mechanism, no adjoint Wilson-line modulus associated with this
breaking appears. Since, locally, SU(5) remains a good symmetry everywhere, no
UV-sensitive threshold corrections arise and SU(5)-violating local operators
are forbidden. Doublet-triplet splitting can be addressed in the context of a
6d N=2 super Yang-Mills theory with gauge group SU(6). If this symmetry is
first broken to SU(5) at a fixed point and then further reduced to the standard
model group in the above non-local way, the two light Higgs doublets of the
MSSM are predicted by the group-theoretical and geometrical structure of the
model.
