## Critical behavior of the PT-symmetric iφ^3 quantum field theory

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)