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A nonperturbative Schwinger-Dyson analysis of mass generation is presentedfor a non-Hermitian PT-symmetric field theory in four dimensions of an axioncoupled to a Dirac fermion.The model is motivated by phenomenologicalconsiderations.The axion has a quartic self-coupling $\lambda$ and a Yukawacoupling $g$ to the fermion. The Schwinger-Dyson equations are derived for themodel with generic couplings. In the non-Hermitian case there is an additionalnonperturbative contribution to the scalar mass. In a simplified rainbowanalysis the solutions for the SD equations, are given for different regimes ofthe couplings $g$ and $\lambda$.

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