Spontaneous CP violation and the strong CP problem

We derive sufficient conditions that guarantee a robust solution of the strong CP problem in theories with spontaneous CP violation, and introduce a class of models satisfying these requirements. In the simplest scenarios the dominant contribution to the topological angle arises at 3-loop order in the Standard Model Yukawa couplings. A variety of new realizations are obtained on a warped extra dimension, which can dynamically generate a CKM phase of the right size as well as the Planck-TeV hierarchy. Experimental signatures of this approach to the strong CP problem include a characteristic pattern of flavor violation and vector-like partners of the top and/or bottom quarks.