Related papers: Derivation of a Gradient Flow from ERG
The quantum field theory of two-dimensional sigma models with bulk and boundary couplings provides a natural framework to realize and unite different species of geometric flows that are of current interest in mathematics. In particular, the…
The energy gradient theory was proposed in our previous studies. The mechanism of flow instability is very different in shear driven flows from pressure driven flows. In present paper, the relationship for the energy variation, work done,…
In this review we consider the concept of limit cycles in the renormalization group flows. The examples of this phenomena in the quantum mechanics and field theory will be presented.
By choosing appropriate generators for the Similarity Renormalization Group (SRG) flow equations, different patterns of decoupling in a Hamiltonian can be achieved. Sharp and smooth block-diagonal forms of phase-shift equivalent…
Holographic renormalization group flows can be interpreted in terms of effective field theory. Based on such an interpretation, a formula for the running scaling dimensions of gauge-invariant operators along such flows is proposed. The…
The renormalization group flow recently found by Br\'ezin and Zinn- Justin by integrating out redundant entries of the $(N+1)\times (N+1)$ hermitian random matrix is studied. By introducing explicitly the RG flow parameter, and adding…
Scheme independence of exact renormalization group equations, including independence of the choice of cutoff function, is shown to follow from general field redefinitions, which remains an inherent redundancy in quantum field theories.…
We present a variational renormalization group (RG) approach using a deep generative model based on normalizing flows. The model performs hierarchical change-of-variables transformations from the physical space to a latent space with…
The inconsistency between the fixed-order (FO) and contour-improved (CI) representation of the QCD corrections to the inclusive hadronic tau decay width limits the precision to which the strong coupling can be determined from this process.…
This article overviews how gradient flows, and discretizations thereof, are useful to design and analyze optimization and sampling algorithms. The interplay between optimization, sampling, and gradient flows is an active research area; our…
We employ the functional renormalization group approach formulated on the Schwinger-Keldysh contour to calculate real-time correlation functions in scalar field theories. We provide a detailed description of the formalism, discuss suitable…
A field theoretic renormalization group method is presented which is capable of dealing with crossover problems associated with a change in the upper critical dimension. The method leads to flow functions for the parameters and coupling…
We examine the precise connection between the exact renormalisation group with local couplings and the renormalisation of correlation functions of composite operators in scale-invariant theories. A geometric description of theory space…
We calculate the two-loop renormalization group (RG) beta-function of a massless scalar field theory from the irreducible version of Polchinski's exact RG flow equation. To obtain the correct two-loop result within this method, it is…
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…
We discuss the following proposition: Renormalization Group flow of quantum theory with a biased symmetry exhibits a fixed hypersurface at which the symmetry is exact. Such emergent symmetries may have important phenomenological…
In effective field theories, the concept of renormalization of perturbative divergences is replaced by renormalization group concepts such as relevance and universality. Universality is related to cutoff scheme independence in…
We show that the exact RG-flow equation introduced recently in hep-th/0207134 can be obtained in the sharp cut-off limit of the well-known ERGE. This can be expected from the fact that in this limit the new scale-dependent effective action…
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…
The Renormalization Group (RG) methods are still far from being completely understood in quenched disordered systems. In order to gain insight into the nature of the phase transition of these systems, it is common to investigate simple…