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

It is pointed out that there exist a few problems to be overcome toward anobservable sub-eV QCD axion in superstring compactification. We give a generalexpression for the axion decay constant. For a large domain wall number$N_{DW}$, the axion decay constant can be substantially lowered from a genericvalue of a scalar singlet VEV. The Yukawa coupling structure in the recent$Z_{12-I}$ model is studied completely, including the needed nonrenormalizableterms toward realistic quark and lepton masses. In this model we find anapproximate global symmetry and vacuum so that a QCD axion results but itsdecay constant is at the GUT scale. The axion-photon-photon coupling iscalculated for a realistic vacuum satisfying the quark and lepton mass matrixconditions. It is the first time calculation of $c_{a\gamma\gamma}$ inrealistic string compactifications: $c_{a\gamma\gamma}={5/3}-1.93\simeq -0.26$.Comment: 33 pages, 2 figures, JHEP format, some errors in the superpotential couplings are corrected and the following discussions are changed correspondingl