  In this mini review, we discuss some recent developments regarding properties
of (quantum) field-theory models containing anti-Hermitian Yukawa interactions
between pseudoscalar fields (axions) and Dirac (or Majorana) fermions.
Specifically, after motivating physically such interactions, in the context of
string-inspired low-energy effective field theories, involving right-handed
neutrinos and axion fields, we proceed to discuss their formal consistency
within the so-called Parity-Time-reversal(PT)-symmetry framework, as well as
dynamical mass generation, induced by the Yukawa interactions, for both
fermions and axions. The Yukawa couplings are assumed weak, given that they are
conjectured to have been generated by non-perturbative effects in the
underlying microscopic string theory. The models under discussion contain, in
addition to the Yukawa terms, also anti-Hermitian anomalous derivative
couplings of the pseudoscalar fields to axial fermion currents, as well as
interactions of the fermions with non-Hermitian axial backgrounds. We discuss
the role of such additional couplings on the Yukawa-induced
dynamically-generated masses. For the case where the fermions are right-handed
neutrinos, we compare such masses with the radiative ones induced by both, the
anti-Hermitian anomalous terms and the anti-Hermitian Yukawa interactions in
phenomenologically relevant models.
