Related papers: Gradient Flow: Perturbative and Non-Perturbative R…
The Renormalization Group flow equations obtained by means of a proper time regulator are used to analyze the restoration of the discrete chiral symmetry at non-zero density and temperature in the Gross-Neveu model in d=2+1 dimensions. The…
These two lectures cover some of the advances that underpin recent progress in deriving continuum solutions from the exact renormalization group. We concentrate on concepts and on exact non-perturbative statements, but in the process will…
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 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…
After a brief review of the definition and properties of the quantum effective Hamiltonian action we describe its renormalization flow by a functional RG equation. This equation can be used for a non-perturbative quantization and study also…
The notion of non-perturbative renormalization is discussed and extended. Within the extended picture, a new non-perturbative representation for the generating functional of Green functions of quantum field theories is suggested. It is…
The previously developed renormalizable perturbative 1/N-expansion in higher dimensional scalar field theories is extended to gauge theories with fermions. It is based on the $1/N_f$-expansion and results in a logarithmically divergent…
In perturbative consideration of the Yang--Mills gradient flow, it is useful to introduce a gauge non-covariant term ("gauge-fixing term") to the flow equation that gives rise to a Gaussian damping factor also for gauge degrees of freedom.…
Machine learning techniques, in particular the so-called normalizing flows, are becoming increasingly popular in the context of Monte Carlo simulations as they can effectively approximate target probability distributions. In the case of…
We initiate the continuum description of a non-perturbative 5d lattice Yang-Mills model with 4d boundaries using the $\varepsilon$-expansion. In its simplest version classically the bulk has an $SU(2)$ gauge symmetry and on the boundary…
In this work, we investigate links between the formulation of the flow of marginals of reversible diffusion processes as gradient flows in the space of probability measures and path wise large deviation principles for sequences of such…
Perturbative and non-perturbative results are presented on the renormalization constants of the quark field and the vector, axial-vector, pseudoscalar, scalar and tensor currents. The perturbative computation, carried out at one-loop level…
We provide a non-technical overview of recent extensions of renormalization methods and techniques to Group Field Theories (GFTs), a class of combinatorially non-local quantum field theories which generalize matrix models to dimension $d…
We review recent developments in the theory of renormalisation group flows in minimal models with boundaries. Among these, we discuss in particular the perturbative calculations of Recknagel et al, not only as a tool to predict the IR…
Various results for higher-order perturbative calculations in the gradient-flow formalism are reviewed, including the gradient-flow beta function and the small-flow-time expansion of the hadronic vacuum polarization and the energy-momentum…
We apply the Symanzik improvement programme to the 4+1-dimensional local re-formulation of the gradient flow in pure $SU(N)$ lattice gauge theories. We show that the classical nature of the flow equation allows to eliminate all cutoff…
We consider the renormalization of theories with many scalar fields. We discuss at the one-loop level some simple, non-gauge models with an arbitrary number of scalars and fermions both in mass-shell and MS schemes. In MS scheme we give a…
We introduce a new family of tensorial field theories by coupling different fields in a non-trivial way, with a view towards the investigation of the coupling between matter and gravity in the quantum regime. As a first step, we consider…
The renormalization group plays an essential role in many areas of physics, both conceptually and as a practical tool to determine the long-distance low-energy properties of many systems on the one hand and on the other hand search for…
We introduce graph normalizing flows: a new, reversible graph neural network model for prediction and generation. On supervised tasks, graph normalizing flows perform similarly to message passing neural networks, but at a significantly…