Real CP violation

We propose a new mechanism called CP to originate spontaneous CP violation. Starting with a CP conserving theory with scalar fields in the adjoint representation of a global or local non-abelian symmetry, we show that even though the VEV's of such scalars are real they give rise to a spontaneous violation of CP. We provide an illustrative example of how this new mechanism of CP violation can give rise to physically significant phases which produce a complex CKM mixing matrix. This mechanism may prove useful in string models with moduli in the adjoint representation as well as in tackling the strong CP problem.