  We investigate the renormalization group flow of the field-dependent Yukawa
coupling in the framework of the three flavor quark-meson model. In a
conventional perturbative calculation, given that the field rescaling is
trivial, the Yukawa coupling does not get renormalized at the one-loop level if
it is coupled to an equal number of scalar and pseudoscalar fields. Its
field-dependent version, however, does flow with respect to the scale. Using
the functional renormalization group technique, we show that it is highly
nontrivial how to extract the actual flow of the Yukawa coupling as there are
several new chirally invariant operators that get generated by quantum
fluctuations in the effective action, which need to be distinguished from that
of the Yukawa interaction.
