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

Abstract

We consider the renormalisation properties of non-Hermitian Yukawa theories involving a pseudoscalar (axion) field. More generally these models provide simple paradigms for the study of the quantum behaviour of non-Hermitian (but PT -symmetric) fermionic models as higher dimensional field theories. The flow between of PT -symmetric and Hermitian fixed points under the renormalisation group flows is examined.

Spontaneous non-Hermiticity in the (2+1)-dimensional Gross-Neveu model

“…Now, taking into account Eqs. (9), it is possible to obtain the T transformations of some Hermitian bispinor forms. In particular,…”

“…(Quite recently, it was noted in Ref. [9] that, perhaps, the phenomenon of spontaneous non-Hermiticity occurs also in some models of Yukawa type.) It means that (i) initial Lagrangian of the massless NJL model is taken to be Hermitian and PT -symmetric, (ii) but, as it was proved in Ref.…”