A note on instantons, $\theta$-dependence and strong CP

I review the standard instanton framework for determining the $\theta$-dependence of instanton-dominated correlation functions in QCD. I then contrast these well-established semiclassical results with the recent assertion of [1,2], that $\theta$-phases are absent and that strong interactions preserve CP for all values of $\theta$. In all scenarios considered, the $\theta$-dependence is shown to be intrinsically non-trivial, being governed either by instantons in the weak-coupling regime or by alternative, non-perturbative considerations when the theory is strongly coupled.