PT symmetric fermionic field theories with axions: Renormalization and dynamical mass generation

Abstract

We consider the renormalization properties of non-Hermitian Yukawa theories involving a pseudoscalar (axion) field at or near four dimensions. The non-Hermiticity is $\mathcal{P}\mathcal{T}$ symmetric where $\mathcal{P}$ is a linear operator (such as parity) and $\mathcal{T}$ is an antilinear idempotent operator (such as time reversal). The coupling constants of the Yukawa and quartic scalar coupling terms reflect this non-Hermiticity. The path integral representing the field theory is used to discuss the Feynman rules associated with the field theory. The fixed point structure associated with the renormalization group has $\mathcal{P}\mathcal{T}$ symmetric and Hermitian fixed points. At two loops in the massless theory, we demonstrate the flow from Hermitian to non-Hermitian fixed points. From the one-loop renormalization of a massive Yukawa theory, a self-consistent Nambu--Jona-Lasinio gap equation is established and its real solutions are discussed.