Related papers: A new approach to piecewise linear Wilson lines
Wilson's formulation of lattice QCD is attractive for many reasons, but perhaps mainly because of its simplicity and conceptual clarity. Numerical simulations of the Wilson theory (and of its improved versions) tend to be extremely…
The transverse-momentum-dependent distributions (TMDs), which are defined by gauge-invariant 3D parton correlators with staple-shaped lightlike Wilson lines, can be calculated from quark and gluon correlators fixed in the Coulomb gauge on a…
We analyze the perturbative cusp and closed polygons of Wilson lines for massless gauge theories in coordinate space, and express them as exponentials of two-dimensional integrals. These integrals have geometric interpretations, which link…
The main aspects of a gauge-invariant approach to the description of quark dynamics in the nonperturbative regime of QCD are first reviewed. In particular, the role of the parallel transport operation in constructing gauge-invariant Green's…
We employ the Transformer to learn patterns in two-dimensional lattice Yang-Mills theory. Specifically, we represent both Wilson loops and their expectation values as tokenized sequences. Taking the shape of Wilson loops as input, the model…
The role of the gauge invariance in noncommutative field theory is discussed. A basic introduction to noncommutative geometry and noncommutative field theory is given. Background invariant formulation of Wilson lines is proposed. Duality…
An old and apparently persistent problem in numerical lattice QCD is that the simulations tend to get trapped in a sector of fixed topological charge when the lattice spacing is taken to zero. The effect sets in very rapidly and may…
In the worldline approach to non-Abelian field theory the colour degrees of freedom of the coupling to the gauge potential can be incorporated using worldline "colour" fields. The colour fields generate Wilson loop interactions whilst…
By using path integral formulation of QCD and QED we prove that the factorization theorem is valid for light-like Wilson line but is not valid for non-light-like Wilson line. This conclusion is shown to be consistent with Ward identity and…
Convolutional networks are large linear systems divided into layers and connected by non-linear units. These units are the "articulations" that allow the network to adapt to the input. To understand how a network manages to solve a problem…
Differential structure of lattices can be defined if the lattices are treated as models of noncommutative geometry. The detailed construction consists of specifying a generalized Dirac operator and a wedge product. Gauge potential and field…
We study the issue of gauge-invariant observables in d=4, N=4 noncommutative gauge theory and UV-IR relation therein. We show that open Wilson lines form a complete set of gauge invariant operators, which are local in momentum space and,…
The smooth piecewise-linear models cover a wide range of applications nowadays. Basically, there are two classes of them: models are transitional or hyperbolic according to their behaviour at the phase-transition zones. This study explored…
We study the gauge theories on noncommutative space. We employ the idea of the covariant position to understand the linear and angular momenta, the center of mass position, and to express all gauge invariant observables including the Wilson…
We discuss the relation between the infrared singularities of on-shell partonic form factors and parton distribution functions (PDFs) near the elastic limit, through their factorisation in terms of Wilson-line correlators. Ultimately we…
In Abelian gauge theories with dynamical matter, Wilson lines can end on the insertions of charged fields. We study the endpoints of Wilson lines in large $N$ bosonic QED$_3$. at its critical point. We first study the stability of an…
The general structure of the perturbative expansion of the vacuum expectation value of a product of Wilson-loop operators is analyzed in the context of Chern-Simons gauge theory. Wilson loops are opened into Wilson lines in order to unravel…
The purpose of this paper is to investigate the global categorical symmetries that arise when gauging finite higher groups in three or more dimensions. The motivation is to provide a common perspective on constructions of non-invertible…
The world-line representation of quantum field theory is a powerful framework for the computation of perturbative multi-leg Feynman amplitudes. In particular, in gauge theories, it provides an efficient way, via point particle Grassmann…
Large-N phase transitions occurring in massive N=2 theories can be probed by Wilson loops in large antisymmetric representations. The logarithm of the Wilson loop is effectively described by the free energy of a Fermi distribution and…