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The Peccei-Quinn (PQ) solution to the strong $CP$ problem requires an anomalous global $U(1)$ symmetry, the PQ symmetry.
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A model discussed in Cheng and Kaplan 2001 also achieve an virtual embedment of the PQ symmetry in a gauged U ( 1 ) U(1) PQ symmetry in an extra dimensional setup
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For other attempts to obtain a high-quality PQ symmetry in the composite axion model, see e.g. Randall 1992 ; Redi and Sato 2016
2016
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