Critical behavior of the PT-symmetric $i{\varphi }^3$ quantum field theory

Abstract

It was shown recently that a PT-symmetric $i{\varphi }^3$ 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 $i{\varphi }^3$ theory has a higher predictive power than the conventional ${\varphi }^3$ theory. A comparison of the $i{\varphi }^3$ model with the Lee-Yang model is given.

arXiv comment8 pages, 1 figure

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• Leading CFT constraints on multi-critical models in d>2
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• Pseudo-Hermitian approach to Goldstone's theorem in non-Abelian non-Hermitian quantum field theories
• Discrete spacetime symmetries and particle mixing in non-Hermitian scalar quantum field theories
• Out-of-time-ordered correlator in non-Hermitian quantum systems
• Massive gauge particles versus Goldstone bosons in non-Hermitian non-Abelian gauge theory
• Direct Higgs-gravity interaction and stability of our Universe
• Poincaré symmetries and representations in pseudo-Hermitian quantum field theory
• Non-Hermitian Yukawa interactions of fermions with axions: potential microscopic origin and dynamical mass generation
• Yang-Lee Zeros of the Yang-Lee Model
• Original study of the $g{\varphi }^2(i\varphi {)}^{\epsilon }$ theory. Analysis of all orders in $\epsilon$ and resummations
• Universal Large-order asymptotic behavior of the Strong-coupling and High-Temperature series expansions
• RG and logarithmic CFT multicritical properties of randomly diluted Ising models
• Anomalous dimensions from conformal field theory: Generalized ${\varphi }^{2n+1}$ theories
• Real critical exponents from the $\epsilon$-expansion in an interacting $U(1)$ model with non-Hermitian $Z_4$ anisotropy
• Non-Hermitian Lagrangian for quasi-relativistic fermions