Vacuum structure and PT -symmetry breaking of the non-Hermetian (iϕ3) theory

Abstract

In this work, we study the PT -symmetric (iϕ3) theory using the effective action formalism. To test the accuracy of the used technique, we apply it first to the PT -symmetric (−ϕ4) theory, where we reproduce the same results obtained in the literature using the method of Dyson-Schwinger equations. In 0 þ 1 spacetime dimensions, the one-loop effective potential prediction for the (iϕ3) theory ought to be more accurate than WKB results. The effective potential for the massless PT -symmetric (iϕ3) model is shown to be bounded from below, which is the first analytic result that advocates the vacuum stability of this theory. Our calculations show that the massless theory possesses only one stable vacuum as in the literature, but for the massive theory we find that there exist two stable vacua. For a nonzero magnetic field, we show that the PT -symmetry of the theory is broken for negative imaginary magnetic field, which agrees with the LeeYang theorem. We argue that PT -symmetry breaking is a manifestation of the Yang-Lee edge singularity