We are players in a theory theater. A play we show here is the 't Hooft mechanism: if a gauge symmetry and a global symmetry are broken by one complex scalar field by the Higgs mechanism then there survives a global symmetry below the breaking scale.
In the string compactification, it is realized when an anomalous gauge U(1) symmetry is created. This is a good example of obtaining a
global PQ symmetry at an intermediate scale, realizing an ``invisible'' axion with mass around $10^{-4}$ eV for a cold dark matter candidate.