Axionic domain wall number related to U(1)$_{\rm anom}$ global symmetry

The QCD axion with $f_a$ at an intermediate scale, 10**9-10**12 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.

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