CP violation in weak interactions from orbifold reduction: Possible unification structures

We present a mechanism to generate complex phases from real 4+1 dimensional couplings in a model of weak interactions through dimensional reduction of a gauge theory. The orbifolding of a 4+1 dimensional Sp(4) \times U(1) group is the minimal setup which provides both CP violation and an SU(2) \times U(1) structure. We show that grand unification requires at least SO