Axionic domain wall number related to U(1)anom global symmetry

The QCD axion with fafa at an intermediate scale, 109 GeV∼1012 GeV109 GeV∼1012 GeV, seems in conflict with the gravity spoil of global symmetries and may face the axionic domain wall problem. We point out that the string compactifications with an anomalous U(1) gauge symmetry, allowing desirable chiral matter spectra, circumvent these two problems simultaneously.