Complete solution to the strong CP problem: Supersymmetric extension of the Nelson-Barr model

We present a supersymmetric solution to the strong $CP$ problem based on spontaneous $CP$ violation which simultaneously addresses the effects coming from supersymmetry breaking. The generated $CP$ violating phase is communicated to the quark sector by interacting with a heavy quark a la Nelson-Barr. The Majorana mass of the right handed neutrinos is generated by interactions with the $CP$ violating sector and so does not conserve $CP$. This gives the neutrino sector a nontrivial $CP$ violating phase which can then generate the baryon asymmetry of the universe through leptogeneis. The problematic phase in the supersymmetry breaking parameters are suppressed by appealing to a particular gauge mediation model which naturally suppresses the phases of the tree-level gluino mass and Higgs bilinear masses. This suppression plus the fact that in gauge mediation all loop generated flavor and $CP$ violation is of the minimal flavor violation variety allows for a complete and consistent solution to the strong $CP$ problem.