Renormalisation group flows connecting a 4 − ϵ dimensional Hermitian field theory to a ΡΤ-symmetric theory for a fermion coupled to an axion

TY - JOUR

T1 - Renormalisation group flows connecting a 4 − ϵ dimensional Hermitian field theory to a ΡΤ-symmetric theory for a fermion coupled to an axion

AU - Croney, Lewis

AU - Sarkar, Sarben

PY - 2023/10/27

Y1 - 2023/10/27

N2 - The renormalisation group flow of a Hermitian field theory is shown to have trajectories which lead to a non-Hermitian Parity-Time (ΡΤ) symmetric field theory for an axion coupled to a fermion in spacetime dimensions D = 4−ϵ, where ϵ > 0. In this renormalisable field theory, the Dirac fermion field has a Yukawa coupling g to a pseudoscalar (axion) field and there is quartic pseudoscalar selfcoupling υ. The robustness of this finding is established by considering flows between ϵ dependent Wilson-Fisher fixed points and also by working to three loops in the Yukawa coupling and to two loops in the quartic scalar coupling. The flows in the neighbourhood of the non-trivial fixed pointsare calculated using perturbative analysis, together with the ϵ expansion. The global flow pattern indicates flows from positive υ to negative υ; there are no flows between real and imaginary g. Using summation techniques we demonstrate a possible non-perturbative ΡΤ-symmetric saddle point forD = 3.

AB - The renormalisation group flow of a Hermitian field theory is shown to have trajectories which lead to a non-Hermitian Parity-Time (ΡΤ) symmetric field theory for an axion coupled to a fermion in spacetime dimensions D = 4−ϵ, where ϵ > 0. In this renormalisable field theory, the Dirac fermion field has a Yukawa coupling g to a pseudoscalar (axion) field and there is quartic pseudoscalar selfcoupling υ. The robustness of this finding is established by considering flows between ϵ dependent Wilson-Fisher fixed points and also by working to three loops in the Yukawa coupling and to two loops in the quartic scalar coupling. The flows in the neighbourhood of the non-trivial fixed pointsare calculated using perturbative analysis, together with the ϵ expansion. The global flow pattern indicates flows from positive υ to negative υ; there are no flows between real and imaginary g. Using summation techniques we demonstrate a possible non-perturbative ΡΤ-symmetric saddle point forD = 3.

M3 - Article

SN - 2470-0010

JO - Physical Review D

JF - Physical Review D

ER -