Related papers: Continuous $\beta$ function for the SU(3) gauge sy…
In completely generic four-dimensional gauge-Yukawa theories, the renormalization group $ \beta $-functions are known to the 3-2-2 loop order in gauge, Yukawa, and quartic couplings, respectively. It does, however, remain difficult to apply…
In an earlier publication, we have introduced a method to obtain, at large N, the effective action for d-dimensional manifolds in a N-dimensional disordered environment. This allowed to obtain the Functional Renormalization Group (FRG)…
In the case of using the higher derivative regularization for $N=1$ SQED with $N_f$ flavors the loop integrals giving the $\beta$-function are integrals of double total derivatives in the momentum space. This feature allows to reduce one of…
Monte Carlo Renormalization Group (MCRG) methods were designed to study the non-perturbative phase structure and critical behavior of statistical systems and quantum field theories. I adopt the 2-lattice matching method used extensively in…
The critical thermodynamics of the two-dimensional N-vector cubic and MN models is studied within the field-theoretical renormalization-group (RG) approach. The beta functions and critical exponents are calculated in the five-loop…
We analyze in detail the renormalization group flows which follow from the recently proposed all orders beta functions for the Chalker-Coddington network model. The flows in the physical regime reach a true singularity after a finite scale…
We further develop an algorithmic and diagrammatic computational framework for very general exact renormalization groups, where the embedded regularisation scheme, parametrised by a general cutoff function and infinitely many higher point…
We study higher order approximations in the renormalization group approach to matrix models. We use constraint equations on the free energy resulting from a freedom of field redefinitionsand obtain the effective beta function for a single…
We present preliminary results of a non-perturbative study of the scale-dependent renormalization constants of a complete basis of Delta F=2 parity-odd four-fermion operators that enter the computation of hadronic B-parameters within the…
I investigate an SU(3) gauge model with 12 fundamental fermions. The physically interesting region of this strongly coupled system can be influenced by an ultraviolet fixed point due to lattice artifacts. I suggest to use a gauge action…
First, we reformulate RG transformations in a recursive way with introduction of an order-parameter field. As a result, we manifest the RG flow of an effective field theory through the emergence of an extra dimensional space, where both RG…
We propose a new strategy for the determination of the step scaling function $\sigma(u)$ in finite size scaling studies using the Gradient Flow. In this approach the determination of $\sigma(u)$ is broken in two pieces: a change of the flow…
Gradient flow has proved useful in the definition and measurement of renormalized quantities on the lattice. Recently, the fact that it suppresses high-modes of the field has been used to construct new, continuous RG transformations both…
We study the renormalization group flows of two-dimensional metrics in sigma models and demonstrate that they provide a continual analogue of the Toda field equations based on the infinite dimensional algebra G(d/dt;1). The resulting Toda…
This PhD thesis is devoted to show that differential renormalization is a simple and useful renormalization method that we can use when dealing with gauge theories. In this work, it is shown how the one-loop results of Constraint…
The renormalization group flow equation obtained by means of a proper time regulator is used to calculate the two loop beta function and anomalous dimension eta of the field for the O(N) symmetric scalar theory. The standard perturbative…
The existence of a strongly coupled ultraviolet fixed point in 4-dimensional lattice models as they cross into the conformal window has long been hypothesized. The SU(3) gauge system with 8 fundamental fermions is a good candidate to study…
Direct verification of the existence of an infinite set of multicritical non-perturbative FPs (Fixed Points) for a single scalar field in two dimensions, is in practice well outside the capabilities of the present standard approximate…
Scenario according to which the SU(2)-gluodynamics is a theory with a nontrivial fixed point is analyzed from the point of view of the modern Monte-Carlo (MC) lattice data. It is found that an assumption of the first order fixed point g=g_f…
The presence of an infinite number of marginal four-fermion operators is a key characteristic of the two-dimensional Gross-Neveu model. In this study, we investigate the structure of UV divergences in this model, and by symmetry argument we…