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We discuss a possibility that a superconformal dynamics induces the emergence of a global U(1)PQ symmetry to solve the strong CP problem through the axion. Fields spontaneously breaking the U(1)PQ symmetry couple to new quarks charged under the ordinary color SU(3)C and a new SU(N) gauge group. The theory flows into an IR fixed point where the U(1)PQ breaking fields hold a large anomalous dimension leading to the suppression of U(1)PQ-violating higher dimensional operators. The spontaneous breaking of the U(1)PQ makes the new quarks massive. The U(1)PQ symmetry is anomalous under the SU(3)C but not under the SU(N) so that the axion couples to only the color SU(3)C and the usual axion potential is generated. We also comment on a model that the U(1)PQ breaking fields are realized as meson superfields in a new supersymmetric QCD.
Nakai et al. (Tue,) studied this question.