Wilsonian approach to the interaction φ2 (iφ)

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We study the renormalization of the non-Hermitian PT-symmetric scalar field theory with the interaction φ2(iφ) using the Wilsonian approach and without any expansion in. Specifically, we solve the Wetterich equation in the local potential approximation, both in the ultraviolet regime and with the loop expansion. We calculate the scale-dependent effective potential and its infrared limit. The theory is found to be renormalizable at the one-loop level only for integer values of, a result which is not yet established within the -expansion. Particular attention is therefore paid to the two interesting cases =1,2, and the one-loop beta functions for the coupling associated with the interaction iφ3 and -φ4 are computed. It is found that the -φ4 theory has asymptotic freedom in four-dimensional spacetime. Some general properties for the Euclidean partition function and n-point functions are also derived.

Original languageEnglish
Article number025007
JournalPhys. Rev. D
Issue number2
Publication statusPublished - 15 Jan 2023


  • hep-th
  • hep-ph
  • quant-ph


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