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 PT symmetric where P is a linear operator (such as parity) and 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 PT 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.