SPONTANEOUS CP VIOLATION AND SUPERSYMMETRY

One way to solve the strong CP problem without axions involves CP being a spontaneously broken symmetry. We discuss certain recent arguments that lend credibility to this idea in the context of superstrings and supersymmetry. We discuss the supersymmetric versions of the so-called Nelson models and show that in them thetaBAR arises at the two-loop level. This implies that the neutron electric dipole moment (EDM) should be near the present limit, whereas the electron electric dipole moment should be unobservably small. On the other hand if CP is not a spontaneously broken symmetry, but explicitly broken, one expects both the neutron and electron EDM's to be not far from the experimental bounds.