Critical behavior of the PT-symmetric $i\phi^3$ quantum field theory

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.