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 at or near $4$ dimensions. The non-Hermiticity is \cPT-symmetric where $\mathcal{P}$ is a linear idempotent operator (such as parity) and $\mathcal{T}$ is an anti-linear 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 renormalisation group has \cPT- 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 renormalisation of a massive Yukawa theory, a self-consistent Nambu-Jona Lasinio gap equation is established and its real solutions are discussed.

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Cited by in corpus (8)

• $\mathcal{P}\mathcal{T}$-symmetric $-g{\phi }^4$ theory
• Exact WKB analysis for $\mathcal{P}\mathcal{T}$ symmetric quantum mechanics: Study of the Ai-Bender-Sarkar conjecture
• Schwinger-Dyson equations and mass generation for an axion theory with a PT symmetric Yukawa fermion interaction
• Renormalisation group flows connecting a $4-\epsilon$ dimensional Hermitian field theory to a $\mathcal{P}\mathcal{T}$-symmetric theory for a fermion coupled to an axion
• Exact quantization conditions and full transseries structures for $\mathcal{P}\mathcal{T}$ symmetric anharmonic oscillators
• Spontaneous non-Hermiticity in the (2+1)-dimensional Thirring model
• Wilsonian approach to the interaction ${\varphi }^2(i\varphi {)}^{\epsilon }$
• Thermodynamic properties of non-Hermitian Nambu--Jona-Lasinio models