Related papers: Proving Abelian dominance in the Wilson loop opera…
We formulate a stochastic gauge fixing method to study the gauge dependence of Abelian projection. In this method, one can change the gauge from the maximally Abelian one to no gauge fixing continuously. We have found that the linear part…
We study the $\mathbb{Z}_2$ and $U(1)$ Abelian lattice gauge theories using a bootstrap method, in which the loop equations and positivity conditions are employed for Wilson loops with lengths $L\leqslant L_{\textrm{max}}$ to derive…
Laplacian Abelian Projection is discussed. This term refers to the use of a new (``Laplacian'') gauge fixing prescription for implementing the Abelian Projection of QCD. The gauge condition is based on the lowest-lying eigenvector of the…
Lattice gauge theories are fundamental to such distinct fields as particle physics, condensed matter or quantum information theory. The recent progress in the control of artificial quantum systems already allows for studying Abelian lattice…
We show that the hypothesis of abelian dominance in maximal abelian gauge, which is known to work for Wilson loops in the fundamental representation, fails for Wilson loops in higher group representations. Monte Carlo simulations are…
Assuming the monopole dominance, that has been proved in the lattice gluodynamics, to hold in the continuum limit, we develop an effective scalar field theory for QCD at large distances to describe confinement. The approach is based on a…
We suggest a new (dynamical) Abelian projection of the lattice QCD. It contains no gauge condition imposed on gauge fields so that Gribov copying is avoided. Configurations of gauge fields that turn into monopoles in the Abelian projection…
We reconsider the properties of the $Q\bar{Q}$ flux tube within Abelian-projected SU(2) lattice gauge theory in terms of electric field and monopole current. In the maximal Abelian gauge we assess the influence of the Gribov copies on the…
The dual superconductor picture is one of the most promising scenarios for quark confinement. To investigate this picture in a gauge-invariant manner, we have proposed a new formulation of Yang-Mills theory, named the decomposition method,…
We investigate the relationship between colour confinement and the monopoles derived from the Cho-Duan-Ge decomposition. These monopoles, unlike Dirac and 't Hooft monopoles, do not require a singular gauge field and are defined for any…
We investigate Abelian and monopole contributions to spatial string tension in the deconfined phase of finite temperature SU(2) gauge theory without imposing any gauge fixing conditions. Lattice calculations of non-Abelian and Abelian…
A simple analytic proof of the formula known as the non-Abelian Stokes theorem is given. It is explicitly shown that the consistency of the formula is guaranteed by the Bianchi identity for the gauge field. An attempt is made to construct…
A comparative study of Abelian and Monopole dominance in the Laplacian and Maximally Abelian projected gauges is carried out. Clear evidence for both types of dominance is obtained for the Laplacian projection. Surprisingly, the evidence is…
In any Abelian gauge theory with an action periodic in the link variables one can perform a duality transformation not only in the partition function, but also in correlation functions including Polyakov loops. The calculation of…
We discuss a particular lattice discretization of abelian gauge theories in arbitrary dimensions. The construction is based on gauging the center symmetry of a non-compact abelian gauge theory, which results in a Villain type action. We…
We show that the nondemolition measurement of a spacelike Wilson loop operator W(C) is impossible in a relativistic non-Abelian gauge theory. In particular, if two spacelike-separated magnetic flux tubes both link with the loop C, then a…
To understand the Abelian dominance and magnetic monopole dominance in low-energy QCD, we rewrite the non-Abelian Wilson loop into the form which is written in terms of its Abelian components or the 't Hooft-Polyakov tensor describing the…
An analysis of the monopole loop length distribution is performed in Wilson-action SU(2) lattice gauge theory. A pure power law in the inverse length is found, at least for loops of length, $l$, less than the linear lattice size $N$. This…
Renormalization group (RG) smoothing is employed on the lattice to investigate and to compare the monopole structure of the SU(2) vacuum as seen in different gauges (maximally Abelian (MAG), Polyakov loop (PG) and Laplacian gauge (LG)).…
We make use of product integrals to provide an unambiguous mathematical representation of Wilson line and Wilson loop operators. Then, drawing upon various properties of product integrals, we discuss such properties of these operators as…