A Scenario for Spontaneous CP Violation in SUSY SO(10)

A scenario is suggested for spontaneous CP violation in non-SUSY and SUSY SU(10). The idea is to have a scalar potential which generates spontaneously a phase, at the high scale, in the VEV that gives a mass to the RH neutrinos. The case of the minimal renormalizable SUSY SO(10) is discussed in detail. The high scale CP breaking induces a phase in the CKM matrix as well. It is also pointed out that, in these models, the scales of Baryogenesis, Seesaw, Spontaneous CP violation and Spontaneous U(1)_QP breaking are all of the same order of magnitude.