Effective action study of the PT-symmetric (iϕ3)6−ϵ theory and the Yang–Lee edge singularity

Abstract

We use the effective potential method to study the PT-symmetric iϕ3 field theory in 6−ϵ space–time dimensions. For ϵ=0, we obtained the first two energy levels which are real as well as reflecting the stability of the spectrum. PT-symmetry breaking occurs at J=0 where the two levels merge and beyond this critical point they have complex values. Since there exist no results in the literature to compare with, we extracted the critical exponents of the theory to test the accuracy of our calculations where we find them agree with exact results from the literature. We showed that the critical point is in fact a Yang–Lee edge singularity which is the first time to link PT-symmetry breaking to the existence of a Yang–Lee edge singularity. For ϵ>0, the fixed point is nontrivial and exists for negative J values as expected from Yang–Lee theory for ferromagnetic systems.