  Among the possible CP-odd couplings of the axion to ordinary matter, the most
relevant ones for phenomenology are the Yukawa couplings to nucleons. We
analyze such non-derivative couplings within three different approaches:
standard effective field theory, the Skyrme model and holographic QCD. In all
the cases, the couplings can be related to the CP-odd non-derivative couplings
to nucleons of the low-lying mesons and the $\eta'$. Using the effective field
theory approach we discuss how to derive the expressions for the CP-odd
interaction terms as functions of the parameters of the effective Lagrangian at
generic number of colors $N_c$ and flavors $N_f$. Then, we compute the CP-odd
couplings to nucleons of the axion, the $\eta'$ and the pseudo-Goldstone mesons
in both the Skyrme and the holographic QCD model with $N_f=2,3$. We present
model-independent expressions for the coefficients of the non-derivative
axion-nucleon couplings. This allows us to provide quantitative estimates of
these couplings.
