Related papers: Study of the Six-Loop Beta Function of the $\lambd…
The strong evidence for the `triviality' of (lambda Phi^4)_4 theory is not incompatible with spontaneous symmetry breaking. Indeed, for a `trivial' theory the effective potential should be given exactly by the classical potential plus the…
Conventional wisdom holds that no four-dimensional gravity field theory can be ultraviolet finite. This understanding is based mainly on power counting. Recent studies confirm that one-loop N = 8 supergravity amplitudes satisfy the…
In this work, we use a specific parameterization of the hypergeometric approximants ( the one by Mera et.al in Phys. Rev. Let. 115, 143001 (2015)) to approximate the seven-loop critical exponent $\nu$ for the $O(2)$-symmetric $\phi^4$…
In a previous paper we derived a relation between the operator product coefficients and anomalous dimensions. We explore this relation in the $(\phi^4)_4$ theory and compute the coefficient functions in the products of $\phi^2$ and $\phi^4$…
We investigate Non-Hermitian quantum field theoretic model with $\iota g\phi^3$ interaction in 6 dimension. Such a model is PT-symmetric for the pseudo scalar field $\phi$. We analytically calculate the 2-loop $\beta$ function and analyse…
The two loop effective potential of massless $\lambda\phi^4$ theory was presented in several regularization and renormalization prescriptions and the dynamical symmetry breaking solution was obtained in strong coupling situation in several…
We consider a vectorial, asymptotically free gauge theory and analyze the effect of higher-loop corrections to the beta function on the evolution of the theory from the ultraviolet to the infrared. We study the case in which the theory…
We provide the reader with a (very) short review of recent advances in our understanding of the $\pi$-dependent terms in massless (Euclidean) 2-point functions as well as in generic anomalous dimensions and $\beta$-functions. We extend the…
We present a self-consistent calculation of the finite temperature effective potential for $\lambda \phi^4$ theory, using the composite operator effective potential in which an infinite series of the leading diagrams is summed up. Our…
We consider an asymptotically free vectorial SU($N_c$) gauge theory with $N_f$ fermions in the fundamental representation and analyze higher-loop contributions to the evolution of the theory from the ultraviolet to the infrared in the limit…
We discuss the calculation of the 1-loop effective action on four dimensional, canonically deformed Euclidean space. The theory under consideration is a scalar $\phi^4$ model with an additional oscillator potential. This model is known to…
In this paper, we consider the $\beta$ function at one-loop approximation for noncommutative scalar QED. The renormalization of the full theory, including the basic vertices, and the renormalization group equation are fully established.…
Summation of the perturbation series for the Gell-Mann--Low function \beta(g) of \phi^4 theory leads to the asymptotics \beta(g)=\beta_\infty g^\alpha at g\to\infty, where \alpha\approx 1 for space dimensions d=2,3,4. The natural hypothesis…
The renormalization group method is applied to the three-loop effective potential of the massive $\phi^4$ theory in the $\bar{\rm MS}$ scheme in order to obtain the next-next-next-to-leading logarithm resummation. For this, we exploit…
We develop a systematic perturbative expansion and compute the one-loop two-points, three-points and four-points correlation functions in a non-commutative version of the U(N) Wess-Zumino-Witten model in different regimes of the…
Effective potential for scalar $\lambda\phi^4$ theory is obtained using the exact renormalization group method which includes both the usual one-loop contribution as well as the dominant higher loop effects. Our numerical calculation…
The structure of loop corrections is examined in a scalar field theory on a three dimensional space whose spatial coordinates are noncommutative and satisfy SU(2) Lie algebra. In particular, the 2- and 4-point functions in $\phi^4$ scalar…
It is commonly stated that because terms in the beta function of a theory at the level of $\ell \ge 3$ loops and higher are scheme-dependent, it is possible to define scheme transformations that can be used to remove these terms, at least…
In the recent years, field theory on non-commutative (NC) spaces has attracted a lot of attention. Most literature on this subject deals with perturbation theory, although the latter runs into grave problems beyond one loop. Here we present…
To investigate the non-perturbative, electric sector of a deconfined gauge theory at nonzero temperature, we consider a SU(2) matrix model. We compute beta-functions to one loop order for the simplest extension of the O(4) nonlinear sigma…