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We develop a geometric framework to analyze quark confinement in four-dimensional Euclidean $SU(2)$ Yang--Mills theory in terms of finite-action topological defects. Starting from self-dual Yang--Mills configurations, we restrict to…
We have proposed the non-Abelian dual superconductivity in SU(3) Yang-Mills theory for the mechanism of quark confinement,and we presented the numerical evidences in preceding lattice conferences by using the proposed gauge link…
A random vortex world-surface model for the infrared sector of Sp(2) Yang-Mills theory is constructed. The Sp(2) gauge group, while allowing for the same set of center vortex fluxes as the SU(2) gauge group, induces a significantly…
Three closely related issues will be discussed. Magnetic quarks having non-Abelian charges have been found recently to appear as the dominant infrared degrees of freedom in some vacua of softly broken N=2 supersymmetric QCD with SU(n_c)…
Magnetic excitations play a crucial role in understanding the color confinement of $4$d Yang-Mills theory, and we have the monopole and the center vortex as plausible candidates to explain its mechanism. Under suitable compactified setups…
We investigate the connection between Color Confinement and thermal Abelian monopoles populating the deconfined phase of SU(2) Yang-Mills theory, by studying how the statistical properties of the monopole ensemble change as the…
In oder to investigate quark confinement, we give a new reformulation of the $SU(N)$ Yang-Mills theory on a lattice and present the results of the numerical simulations of the $SU(3)$ Yang-Mills theory on a lattice. The numerical…
We propose and analyze a new method of detecting center vortices and monopoles in lattice Yang-Mills theory. This procedure is sensitive to the intrinsic degeneracy of the center charges, which play a crucial role in how these topological…
A model for the infrared sector of SU(2) Yang-Mills theory, based on magnetic vortex degrees of freedom represented by (closed) random world-surfaces, is presented. The model quantitatively describes both the confinement properties…
The center vortex model for the infrared sector of Yang-Mills theory, previously studied for the SU(2) gauge group, is extended to SU(3). This model is based on the assumption that vortex world-surfaces can be viewed as random surfaces in…
We prove Abelian magnetic monopole dominance in the string tension of QCD. Abelian and monopole dominance in low energy physics of QCD has been confirmed for various quantities by recent Monte Carlo simulations of lattice gauge theory. In…
We extend the approach of Banks, Myerson, and Kogut for the calculation of the Wilson loop in lattice U(1) to the non-abelian SU(2) group. The original degrees of freedom of the theory are integrated out, new degrees of freedom are…
We discuss relation between lattice phenomenology of confining fields in the vacuum state of Yang-Mills theories (mostly SU(2) case) and continuum theories. In the continuum, understanding of the confinement is most straightforward in the…
The dual superconductivity is a promising mechanism for quark confinement. We have presented a new formulation of the Yang-Mills theory on the lattice that enables us to change the original non-Abelian gauge field into the new field…
In this paper we begin on a new lattice formulation of the non-linear change of variables called the Cho--Faddeev--Niemi decomposition in SU(2) Yang-Mills theory. This is a compact lattice formulation improving the non-compact lattice…
We find that Polyakov lines, computed in abelian-projected SU(2) lattice gauge theory in the confined phase, have finite expectation values for lines corresponding to two units of the abelian electric charge. This means that the…
We give a definition of gauge-invariant magnetic monopoles in Yang-Mills theory without using the Abelian projection due to 't Hooft. They automatically appear from the Wilson loop operator. This is shown by rewriting the Wilson loop…
Recently, we have developed a reformulation of the lattice Yang-Mills theory based on the change of variables a la Cho-Faddeev-Niemi combined with a non-Abelian Stokes theorem. In this talk, we give a new procedure (called reduction) for…
The question whether the center vortex picture of the strongly interacting vacuum can encompass the infrared dynamics of both SU(2) as well as Sp(2) Yang-Mills theory is addressed. These two theories contain the same center vortex degrees…
We study, by means of numerical lattice simulations, the properties of the reconfinement phase transition taking place in trace deformed $SU(3)$ Yang-Mills theory defined on $\mathbb{R}^3\times S^1$, in which center symmetry is recovered…