The limits of the strong CP problem

While CP violation has never been observed in the strong interactions, the QCD Lagrangian admits a CP-odd topological interaction proportional to the so called θ angle, which weighs the contributions to the partition function from different topological sectors. The observational bounds are usually interpreted as demanding a severe tuning of θ against the phases of the quark masses, which constitutes the strong CP problem. Here we report on recent challenges to this view based on a careful treatment of boundary conditions in the path integral and of the limit of infinite spacetime volume, which leads to θ dropping out of fermion correlation functions and becoming unobservable, implying that CP is preserved in QCD.