A Solution to the Small Phase Problem of Supersymmetry

It is a well--known problem that in supersymmetric models there are new CP--violating phases which, if unsuppressed, would give a neutron electric dipole moment $10^2$ to $10^3$ times the present experimental limit. Here we propose that these new phases are suppressed by CP invariance, which is broken spontaneously at a high scale and that this breaking shows up at low energies only through a universal phase of the gaugino masses. It is shown that this can well fit both $\epsilon$ and $\epsilon^\prime$ of the neutral Kaon system. The electric dipole moments of the neutron and the electron should be not much below present limits. A model incorporating these ideas in a very economical way is presented.