Modification of decay constants of superstring axions: Effects of flux compactification and axion mixing

We study possibilities for lowering the decay constants of superstring axions. In the heterotic Calabi-Yau compactification, a localized model-dependent axion can appear at a nearly collapsing 2-cycle. The effect of flux can be used for generating warp factor suppression of the axion decay constant. We also point out that the hidden sector instanton potential much higher than the QCD instanton potential picks up the larger effective axion decay constant as that of the QCD axion. We show that this can be converted by introducing many the hidden-sector quarks so that the decay constant of the QCD axion turns out to be much smaller than the string scale