Related papers: Gradient flow and the renormalization group
The renormalization group (RG) equation in the self-consistent local potential approximation (SC-LPA) suggested earlier for the description of continuous phase transitions in lattice models of the Landau-Ginzburg type has been applied to…
We study higher derivative extension of the functional renormalization group (FRG). We consider FRG equations for a scalar field that consist of terms with higher functional derivatives of the effective action and arbitrary cutoff…
The paper is an attempt to relate two vast areas of the applicability of the renormalization group (RG): field theoretic models and partial differential equations. It is shown that the Green function of a nonlinear diffusion equation can be…
We develop a perturbative formulation of the Ricci flow in gravity. Following steps analogous to the gradient flow in QCD, we supplement the usual Feynman rules for perturbative gravity by flowed propagators and vertices as well as graviton…
In the context of Wilsonian Renormalization, renormalization group (RG) flows are a set of differential equations that defines how the coupling constants of a theory depend on an energy scale. These equations closely resemble…
We apply the functional renormalization group to Starobinsky's stochastic equation describing the local dynamics of a light scalar field in de Sitter. After elaborating on the over-damped regime of stochastic dynamics, we introduce an…
We introduce Wilson's, or Polchinski's, exact renormalization group, and review the Local Potential Approximation as applied to scalar field theory. Focusing on the Polchinski flow equation, standard methods are investigated, and by…
In the present article we analyze Non-Perturbative Renormalization Group flow equations in the order phase of $\mathbb{Z}_2$ and $O(N)$ invariant scalar models in the derivative expansion approximation scheme. We first address the behavior…
We prove local existence of solutions of a functional Renormalisation Group equation for the effective action of an interacting quantum field theory, when a suitable Local Potential Approximation is considered. To obtain this equation in a…
We review the application of field-theoretic renormalization group (RG) methods to the study of fluctuations in reaction-diffusion problems. We first investigate the physical origin of universality in these systems, before comparing RG…
The Renormalization Group Flow Equations of the Scalar-QED model near Planck's scale are computed within the framework of the average effective action. Exact Flow Equations, corrected by Einstein Gravity, for the running self-interacting…
The one-loop renormalization of the action for a set Dirac fermions and a set of scalars spanning an arbitrary manifold coupled via Yukawa-like and gauge interactions is presented. The computation is performed with functional methods and in…
A gradient flow equation for $\lambda\phi^{4}$ theory in $D=4$ is formulated. In this scheme the gradient flow equation is written in terms of the renormalized probe variable $\Phi(t,x)$ and renormalized parameters $m^{2}$ and $\lambda$ in…
These lectures contain an introduction to modern renormalization group (RG) methods as well as functional RG approaches to gauge theories. In the first lecture, the functional renormalization group is introduced with a focus on the flow…
The gradient flow exact renormalization (GFERG) is a variant of the exact renormalization group of gauge theory that aims to preserve gauge symmetry as manifestly as possible. From an integral representation of the Wilson action in GFERG…
We discuss structural aspects of the functional renormalisation group. Flows for a general class of correlation functions are derived, and it is shown how symmetry relations of the underlying theory are lifted to the regularised theory. A…
Working in scalar field theory, we consider RG trajectories which correspond to nonrenormalizable theories, in the Wilsonian sense. An interesting question to ask of such trajectories is, given some fixed starting point in parameter space,…
The gradient property of the renormalisation group (RG) flow of multiscalar theories is examined perturbatively in $d=4$ and $d=4-\varepsilon$ dimensions. Such theories undergo RG flows in the space of quartic couplings $\lambda^I$.…
The field theoretic renormalization group (RG) and the operator product expansion (OPE) are applied to the model of a density field advected by a random turbulent velocity field. The latter is governed by the stochastic Navier-Stokes…
We employ deep neural networks to represent the field derivative of the scale-dependent effective potential in the functional renormalization group (fRG) framework for nonperturbative quantum field theory. By embedding the fRG flow…