Schwinger-Dyson equations and mass generation for an axion theory with a PT symmetric Yukawa fermion interaction

A nonperturbative Schwinger-Dyson analysis of mass generation is presented for a non-Hermitian PT -symmetric field theory in four dimensions of an axion coupled to a Dirac fermion. The model is motivated by phenomenological considerations. The axion has a quartic self-coupling λ and a Yukawa coupling g to the fermion. The Schwinger-Dyson equations are derived for the model with generic couplings. In the non-Hermitian case there is an additional nonperturbative contribution to the scalar mass. In a simplified rainbow analysis the solutions for the SD equations, are given for different regimes of the couplings g and λ.