Related papers: The Holographic Renormalization Group
By applying the holographic method, we study a non-perturbative renormalization group (RG) flow triggered by a gluon condensate. After introducing a bulk scalar field in an AdS space related to the gluon condensate, we investigate the trace…
I discuss collinear and infrared divergences in QCD cross sections with massless and massive final-state particles. I present the two-loop renormalization group evolution and resummation in terms of anomalous dimensions, and I show specific…
In the following text we introduce the concept of pseudo-codecomposition of a transformation group, also we show the collection of all transformation groups pseudo-codecomposable to distal ones is a proper intermediate class of the class of…
Large-$N$ renormalization group equations for one- and two-matrix models are derived. The exact renormalization group equation involving infinitely many induced interactions can be rewritten in a form that has a finite number of coupling…
A geometric derivation of nonholonomic integrators is developed. It is based in the classical technique of generating functions adapted to the special features of nonholonomic systems. The theoretical methodology and the integrators…
We propose a local renormalization group procedure where length scale is changed in spacetime dependent way. Combining this scheme with an earlier observation that high energy modes in renormalization group play the role of dynamical…
We give an overview of differential cohomology from the point of view of algebraic topology. This includes a survey of several different definitions of differential cohomology groups, a discussion of differential characteristic classes, an…
We review the formalism of holographic renormalization. We start by discussing mathematical results on asymptotically anti-de Sitter spacetimes. We then outline the general method of holographic renormalization. The method is illustrated by…
The results of the renormalization group are commonly advertised as the existence of power law singularities near critical points. The classic predictions are often violated and logarithmic and exponential corrections are treated on a…
In this paper we give an overview of some recent progress in using holography to study various far-from-equilibrium condensed matter systems. Non-equilibrium problems are notoriously difficult to deal with, not to mention at strong coupling…
We apply the real space Renormalisation Group (RNG) technique to a variety of one-dimensional Ising chains. We begin by recapitulating the work of Nauenberg for an ordered Ising chain, namely the decimation approach. We extend this work to…
We discuss some higher-loop studies of renormalization-group flows and fixed points in various quantum field theories.
Renormalization group method is one of the most powerful tool to obtain approximate solutions to differential equations. We apply the renormalization group method to Hamiltonian systems whose integrable parts linearly depend on action…
In a series of papers, we investigate the reformulation of Epstein-Glaser renormalization in coordinate space, both in analytic and Hopf algebraic terms. This first article deals with analytical aspects. Some of the historically good…
In this paper we explore the method of holomorphic induction for unitary representations of Banach--Lie groups. First we show that the classification of complex bundle structures on homogeneous Banach bundles over complex homogeneous spaces…
Using as an example the Einstein gravity with the cosmological constant, we discuss the calculation of renormalization group functions off shell. We found, that gauge dependent terms should be absorbed by the nonlinear renormalization of…
We classify the domains of holomorphy of all Harish-Chandra modules of irreducible unitary representations of simple non-compact Lie groups.
Quantum field theories require a cutoff to regulate divergences that result from local interactions, and yet physical results can not depend on the value of this cutoff. The renormalization group employs a transformation that changes the…
We expand the class of polarizable Carnot groups by implementing a technique to polarize anisotropic Heisenberg groups.
A recently proposed renormalization group approach to dimensional crossover in quasi-one-dimensional quantum antiferromagnets is improved and then shown to give identical results, in some cases, to those obtained earlier.