Carl M. Bender, V. Branchina, Emanuele Messina

It was shown recently that a PT-symmetric \(i\phi^3\) quantum field theory in \(6-\epsilon\) dimensions possesses a nontrivial fixed point. The critical behavior of this theory around the fixed point is examined and it is shown that the corresponding phase transition is related to the existence of a nontrivial solution of the gap equation. The theory is studied first in the mean-field approximation and the critical exponents are calculated. Then, it is examined beyond the mean-field approximation by using renormalization-group techniques, and the critical exponents for \(6-\epsilon\) dimensions are calculated to order \(\epsilon\). It is shown that because of its stability the PT-symmetric \(i\phi^3\) theory has a higher predictive power than the conventional \(\phi^3\) theory. A comparison of the \(i\phi^3\) model with the Lee-Yang model is given.

http://arxiv.org/abs/1301.6207

High Energy Physics – Theory (hep-th); Mathematical Physics (math-ph); Quantum Physics (quant-ph)