  We study the renormalization group running of axion couplings while taking
into account that the Standard Model can be extended to its supersymmetric
extension at a certain energy scale below the axion decay constant. We then
apply our results to three different classes of axion models, i.e. KSVZ-like,
DFSZ-like, and string-theoretic axions, and examine if string-theoretic axions
can be distinguished from others by having a different pattern of low energy
couplings to the photon, nucleons and electron. We find that the low energy
couplings of string-theoretic axions have a similar pattern as those of
KSVZ-like axions but yet reveal a sizable difference which might be testable in
future axion search experiments. We also note that the coupling of KSVZ-like
QCD axions to the electron is dominated by a three-loop contribution involving
the exotic heavy quark, gluons, top quark and Higgs field.
