Related papers: Two-Loop Diagrams in Noncommutative $\phi^4_4$ the…
In this paper we investigate the Schwinger parametric representation for the Feynman amplitudes of the recently discovered renormalizable $\phi^4_4$ quantum field theory on the Moyal non commutative ${\mathbb R^4}$ space. This…
A new method is developed to calculate multiloop Feynman diagrams in non-relativistic field theories. A consistent scheme for regularizing and renormalizing loop integrals is established and shown to reproduce the results of dimensional…
For theories with multiple couplings we construct simple expressions for the four-dimensional (or, in general, integer-dimensional) renormalization constants assuming that all divergences are logarithmical. These expressions allow relating…
The five-loop effective potential and the associated summation of subleading logarithms for O(4) globally-symmetric massless $\lambda\phi^4$ field theory in the Coleman-Weinberg renormalization scheme $\frac{d^4V}{d\phi^4}|_{\phi = \mu} =…
For the general renormalizable ${\cal N}=1$ supersymmetric gauge theory we investigate renormalization of the Faddeev--Popov ghosts using the higher covariant derivative regularization. First, we find the two-loop anomalous dimension…
A convenient integral representation for zig-zag four-point and two-point planar Feynman diagrams relevant to the bi-scalar D-dimensional fishnet field theory is obtained. This representation gives a possibility to evaluate exactly diagrams…
We point out that there is a missing portion in the two-loop effective potential of the massless O(N) phi^4 theory obtained by Jackiw in his classic paper, Phys. Rev. D 9, 1686 (1974).
We present the result of a full direct component calculation for the planar four-loop anomalous dimension of the Konishi operator in N =4 Supersymmetric Yang-Mills theory. Our result confirms the results obtained from superfield…
We present a systematic investigation of one-loop renormalizability for nonanticommutative N=1/2, U(N) SYM theory in superspace. We first discuss classical gauge invariance of the pure gauge theory and show that in contradistinction to the…
We perform a supergraph computation of the effective Kaehler potential at one and two loops for general four dimensional N=1 supersymmetric theories described by arbitrary Kaehler potential, superpotential and gauge kinetic function. We…
In this work, we employ a field-theoretic renormalization group approach to study a paradigmatic model of directed percolation. We focus on the perturbative calculation of the equation of state, extending the analysis to the three-loop…
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 $\phi^4$…
Evaluation of three- and four-point diagrams with massless internal particles and arbitrary external momenta is considered. Exact results for some two-loop diagrams (planar and non-planar three-point contributions and the "double box"…
We compute the anomalous dimensions of a set of composite operators which involve derivatives at four loops in MSbar in phi^4 theory as a function of the operator moment n. These operators are similar to the twist-2 operators which arise in…
We recalculate four-loop renormalization group functions in 2-dimensional nonlinear O(n) {\sigma}-model using coordinate-space method. The high accuracy of calculation allow us to find the analytical form of {\beta}- and {\gamma}-function…
The renormalization group functions are calculated in $D=4-\epsilon$ dimensions for the $\phi^4$-theory with two coupling constants associated with an ${O}(N)$-symmetric and a cubic interaction. Divergences are removed by minimal…
We perform a systematic study of the one-loop renormalizability of all Poisson-Lie T-dualizable $\si$-models with two-dimensional targets. We show that whatever Drinfeld double and whatever matrix of coupling constants we consider the…
We review several multi-loop techniques for analytical massless Feynman diagram calculations in relativistic quantum field theories: integration by parts, the method of uniqueness, functional equations and the Gegenbauer polynomial…
It has been proposed that the noncommutative geometry of the "fuzzy" 2-sphere provides a nonperturbative regularization of scalar field theories. This generalizes to compact Kaehler manifolds where simple field theories are regularized by…
We reconsider the perturbative expansion of the Wilson loop in 2d noncommutative gauge theories, using an improved integration method. For the class of maximally crossed diagrams in the $\theta \to \infty$ limit we find an intriguing…