Wilsonian approach to the interaction φ2 (iφ)

TY - JOUR

T1 - Wilsonian approach to the interaction φ2 (iφ)

AU - Ai, Wen-Yuan

AU - Alexandre, Jean

AU - Sarkar, Sarben

N1 - Funding Information: This work is supported by the UK Engineering and Physical Sciences Research Council (Grant No. EP/V002821/1), and the Science and Technology Facilities Council (Grant No. STFC-ST/T000759/1). Publisher Copyright: © 2023 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.

PY - 2023/1/15

Y1 - 2023/1/15

N2 - 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.

AB - 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.

KW - hep-th

KW - hep-ph

KW - quant-ph

UR - http://www.scopus.com/inward/record.url?scp=85147152845&partnerID=8YFLogxK

U2 - 10.1103/PhysRevD.107.025007

DO - 10.1103/PhysRevD.107.025007

M3 - Article

VL - 107

JO - Phys. Rev. D

JF - Phys. Rev. D

IS - 2

M1 - 025007

ER -