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

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Original languageEnglish
Article number015009
JournalPhysical Review D
Volume106
Issue number1
DOIs
Accepted/In press21 Jun 2022
Published12 Jul 2022

Bibliographical note

Funding Information: The work of N. E. M. and S. S. is supported in part by the UK Science and Technology Facilities research Council (STFC) and UK Engineering and Physical Sciences Research Council (EPSRC) under the research Grants No. ST/T000759/1 and No. EP/V002821/1, respectively. N. E. M. acknowledges participation in the COST Association Action CA18108 Quantum Gravity Phenomenology in the Multimessenger Approach (QG-MM). We would like to thank Carl Bender and Wen-Yuan Ai for valuable discussions. Publisher Copyright: © 2022 authors. Published by the American Physical Society. Published by the American Physical Society under the terms of the "https://creativecommons.org/licenses/by/4.0/"Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Funded by SCOAP3.

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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.

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