Related papers: The Renormalization Group with Exact beta-Function…
The "exact" or "functional" renormalization group equation describes the renormalization group flow of the effective average action $\Gamma_k$. The ordinary effective action $\Gamma_0$ can be obtained by integrating the flow equation from…
In a physical renormalization scheme, gauge couplings are defined directly in terms of physical observables. Such effective charges are analytic functions of physical scales, and thus mass thresholds are treated with their correct analytic…
We study conformal quantum mechanics by first considering the perturbative $S$-matrix in various dimensions. The model has two couplings and we study perturbatively the degree of ultraviolet divergences arising in the interplay between the…
Some calculations in supersymmetric theories, made with the higher derivative regularization, show that the beta-function is given by integrals of total derivatives. This is qualitatively explained for the N=1 supersymmetric electrodynamics…
Yang-Mills theory in the first order formalism appears as the deformation of a topological field theory, the pure BF theory. We discuss this formulation at the quantum level, giving the Feynman rules of the BF-YM theory, the structure of…
We derive asymptotic freedom and the $SU(3)$ Yang-Mills $\beta$-function using the renormalization group procedure for effective particles. In this procedure, the concept of effective particles of size $s$ is introduced. Effective particles…
We propose various properties of renormalization group beta functions for vector operators in relativistic quantum field theories. We argue that they must satisfy compensated gauge invariance, orthogonality with respect to scalar beta…
The short-distance asymptotics of the generating functional for $n$-point correlators of twist-$2$ operators in $\mathcal{N}=1$ supersymmetric (SUSY) SU($N$) Yang-Mills (SYM) theory were recently calculated in [1,2]. This calculation…
We determine the missing finite-size corrections to the asymptotic one-loop dilatation operator of the real $\beta$-deformed $\mathcal{N}=4$ SYM theory for the gauge groups $U(N)$ and $SU(N)$ in the 't Hooft limit. In the $SU(N)$ case, the…
We investigate the renormalisation of Einstein gravity using a novel subtraction scheme in dimensional regularisation. The one-loop beta function for Newton's constant receives contributions from poles in even dimensions and can be mapped…
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 discuss the perturbative running Yang-Mills coupling constant in the Wilsonian exact renormalization group approach, and compare it to the running coupling in the more conventional MS-bar scheme. The exact renormalization group approach…
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…
We have developed a nonperturbative functional renormalization group approach for random field models and related disordered systems for which, due to the existence of many metastable states, conventional perturbation theory often fails.…
We show how to consistently renormalize $\mathcal{N} = 1$ and $\mathcal{N} = 2$ super-Yang-Mills theories in flat space with a local (i.e. space-time-dependent) renormalization scale in a holomorphic scheme. The action gets enhanced by a…
We consider a possibility to unify the methods of regularization, such as the renormalization group method, stochastic quantization etc., by the extension of the standard field theory of the square-integrable functions $\phi(b)\in…
This is the 5-th paper in the series devoted to explicit formulating of the rules needed to manage an effective field theory of strong interactions in S-matrix sector. We discuss the principles of constructing the meaningful perturbation…
We provide a renormalization procedure for Phi-derivable approximations in theories coupling different types of fields. We illustrate our approach on a scalar phi^4 theory coupled to fermions via a Yukawa-like interaction. The…
Functional conjugation methods are used to analyze the global structure of various renormalization group trajectories, and to gain insight into the interplay between continuous and discrete rescaling. With minimal assumptions, the methods…
We consider the dynamics of gauge-Yukawa theories in the presence of a large number of matter constituents. We first review the current status for the renormalization group equations of gauge-fermion theories featuring also semi-simple…