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 [Formula: see text]-symmetric [Formula: see text] field theory in [Formula: see text] space–time dimensions. For [Formula: see text], we obtained the first two energy levels which are real as well as reflecting the stability of the spectrum. [Formula: see text]-symmetry breaking occurs at [Formula: see text] 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 [Formula: see text]-symmetry breaking to the existence of a Yang–Lee edge singularity. For [Formula: see text], the fixed point is nontrivial and exists for negative [Formula: see text] values as expected from Yang–Lee theory for ferromagnetic systems.