Anomalous solutions to the strong CP problem.

We present a new mechanism for solving the strong CP problem using a Z_{2} discrete symmetry and an anomalous U(1) symmetry. A Z_{2} symmetry is used so that two gauge groups have the same theta angle. An anomalous U(1) symmetry makes the difference between the two theta angles physical and the sum unphysical. Two models are presented where the anomalous symmetry manifests itself in the IR in different ways. In the first model, there are massless bifundamental quarks, a solution reminiscent of the massless up quark solution. In the IR of this model, the η^{'} boson relaxes the QCD theta angle to the difference between the two theta angles-in this case zero. In the second model, the anomalous U(1) symmetry is realized in the IR as a dynamically generated mass term that has exactly the phase needed to cancel the theta angle. Both of these models make the extremely concrete prediction that there exist new colored particles at the TeV scale.