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Towards a Dynamical Solution of the Strong CP Problem

It is argued that QCD might solve the strong CP problem on its own. To test this idea, a lattice simulation suggests itself. In view of the difficulty of such a calculation we have, as a first step, investigated the problem in the $CP^3$ model. The $CP^3$ model is in many respects similar to QCD. In this talk I shall present some first results of our calculation. Among other things it is shown that the model has a first order deconfining phase transition in $θ$ and that the critical value of $θ$ decreases towards zero as $β$ is taken to infinity. This suggests that $θ$ is tuned to zero in the continuum limit.