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A general discussion of the renormalization of the quantum theory of a scalar field as an effective field theory is presented. The renormalization group equations in a mass-independent renormalization scheme allow us to identify the…
A careful analysis of differential renormalization shows that a distinguished choice of renormalization constants allows for a mathematically more fundamental interpretation of the scheme. With this set of a priori fixed integration…
The asymptotic structure of gravity in $D=6$ spacetime dimensions is described at spatial infinity in the asymptotically flat context through Hamiltonian (ADM) methods. Special focus is given on the BMS supertranslation subgroup. It is…
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…
The flow equations of the Functional Renormalization Group are applied to the O(N)-symmetric scalar theory, for N=1 and N=4, in four Euclidean dimensions, d=4, to determine the effective potential and the renormalization function of the…
Renormalisation group flows of the bosonic nonlinear \sigma-model are governed, perturbatively, at different orders of \alpha', by the perturbatively evaluated \beta--functions. In regions where \frac{\alpha'}{R_c^2} << 1 the flow equations…
The boundary beta-function generates the renormalization group acting on the universality classes of one-dimensional quantum systems with boundary which are critical in the bulk but not critical at the boundary. We prove a gradient formula…
The behavior of the beta-function of the low-energy effective coupling in the N=2 supersymmetric SU(2) QCD with several massive matter hypermultiplets and in the SU(3) Yang-Mills theory is determined near the superconformal points in the…
The process of renormalization to eliminate divergences arising in quantum field theory is not uniquely defined; one can always perform a finite renormalization, rendering finite perturbative results ambiguous. The consequences of making…
We study the renormalization group flow of higher derivative gravity, utilizing the functional renormalization group equation for the average action. Employing a recently proposed algorithm, termed the universal renormalization group…
The renormalization group (RG) is an essential technique in statistical physics and quantum field theory, which considers scale-invariant properties of physical theories and how these theories' parameters change with scaling. Deep learning…
Bilevel graph structure learning is widely understood to improve graph neural networks by jointly optimizing model parameters and a learned graph structure, with the resulting performance gain attributed to the rewired adjacency. We find…
The stability of nonrelativistic fermionic systems to interactions is studied within the Renormalization Group framework. A brief introduction to $\phi^4$ theory in four dimensions and the path integral formulation for fermions is given.…
We study a self-interacting scalar $\varphi^4$ theory on the $d$-dimensional noncommutative torus. We determine, for the particular cases $d=2$ and $d=4$, the counterterms required by one-loop renormalization. We discuss higher loops in two…
While renormalization groups are fundamental in physics, renormalization of complex networks remains vague in its conceptual definition and methodology. Here, we propose a novel strategy to renormalize complex networks. Rather than…
We demonstrate the full power of nonperturbative renormalisation group methods for nonequilibrium situations by calculating the quantitative phase diagrams of simple branching and annihilating random walks and checking these results against…
Field theoretic renormalization group and the operator product expansion are applied to a model of a passive scalar field, advected by the Gaussian strongly anisotropic velocity field. Inertial-range anomalous scaling behavior is…
The correspondence between the four-dimensional SU(N), $\cN = 4$ SYM taken at large $N$ and the type II B SUGRA on the $AdS_5\times S_5$ background is considered. We argue that the classical equations of motion in the SUGRA picture can be…
The motivation and the challenge in applying the renormalization group for systems with several scaling regimes is briefly outlined. The four dimensional $\phi^4$ model serves as an example where a nontrivial low energy scaling regime is…
We study the statistical properties of observables of scale-free networks in the degree-thresholding renormalization (DTR) flows. For BA scale-free networks with different sizes, we find that their structural and dynamical observables have…