String compactification, QCD axion and axion-photon-photon coupling

It is pointed out that there exist a few problems to be overcome toward an observable sub-eV QCD axion in superstring compactification. We give a general expression for the axion decay constant. For a large domain wall number Now, the axion decay constant can be substantially lowered from a generic value of a scalar singlet VEV. The Yukawa coupling structure in the recent Z_12-1 model is studied completely, including the needed nonrenormalizable terms toward realistic quark and lepton masses. In this model we find an approximate global symmetry and vacuum so that a QCD axion results but its decay constant is at the GUT scale. The axion-photon-photon coupling is calculated with a reasonable assumption on a realistic vacuum satisfying the quark and lepton mass matrix conditions. It is the first time calculation of c _αγγ in realistic string compactifications: C _αγγ= 5/3- 1.93 ≃ -0.26.