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We show that the extended Abelian magnetic monopoles in the Maximal Abelian projection of lattice SU(2) gluodynamics are locally correlated with the magnetic and the electric parts of the SU(2) action density. These correlations are…
We propose a novel type of color magnetic condensation originating from magnetic monopoles so that it provides the mass of off-diagonal gluons in the Yang-Mills theory. This dynamical mass generation enables us to explain the infrared…
We derive a new version of SU(3) non-Abelian Stokes theorem by making use of the coherent state representation on the coset space $SU(3)/(U(1)\times U(1))=F_2$, the flag space. Then we outline a derivation of the area law of the Wilson loop…
We propose to use the different kinds of vacua of the gauge theories coupled to matter as a laboratory to test confinement ideas of pure Yang-Mills theories. In particular, the very poor overlap of the Wilson loop with the broken string…
We study the potential between a static center monopole and antimonopole in 4d SU(2) Yang-Mills theory. Using a new numerical method, we show that the 't Hooft loop is a dual order parameter with respect to the Wilson loop, for the…
The dual Meissner effect is the promising mechanism for quark confinement. We have proposed a new formulation of SU(N) Yang-Mills (YM) theory on a lattice, which can extract the dominant mode for quark confinement in the gauge independent…
We introduce a novel decomposition of the four dimensional SU(2) gauge field. This decomposition realizes explicitely a symmetry between electric and magnetic variables, suggesting a duality picture between the corresponding phases. It also…
By comparision with numerical results in the maximal Abelian projection of lattice Yang-Mills theory, it is argued that the nonperturbative dynamics of Yang Mills theory can be described by a set of fields that take their values in the…
Abelian and center gauges are considered in continuum Yang-Mills theory in order to detect the magnetic monopole and center vortex content of gauge field configurations. Specifically we examine the Laplacian Abelian and center gauges, which…
By using the method of center projection the center vortex part of the gauge field is isolated and its propagator is evaluated in the center Landau gauge, which minimizes the open 3-dimensional Dirac volumes of non-trivial center links…
In earlier work, we used a gauge independent Abelian Decomposition to show that Abelian degrees of freedom are wholly responsible for the static quark potential. The restricted Abelian field can be split into two terms, a Maxwell term and a…
We propose a new version of SU(N) Yang-Mills theory reformulated in terms of new field variables which are obtained by a nonlinear change of variables from the original Yang-Mills gauge field. The reformulated Yang-Mills theory enables us…
In the framework of the center vortex picture of confinement, the nature of the deconfining phase transition is studied. Using recently developed techniques which allow to associate a center vortex configuration with any given lattice gauge…
We give a review on hyperbolic magnetic monopoles and hyperbolic vortices obtained in the unified way through the conformal equivalence by the dimensional reduction from the symmetric instantons with various spatial symmetries in the…
The infrared structure of SU(2) Yang-Mills theory is studied by means of lattice gauge simulations using a new constrained cooling technique. This method reduces the action while all Polyakov lines on the lattice remain unchanged. In…
We investigate the role of monopoles in the deconfinement transition of finite temperature $SU(2)$ QCD in the maximally abelian gauge. In the confinement phase a long monopole loop exists in each configuration, whereas no long loop exists…
We summarize recent nonperturbative results obtained for the thermodynamics of an SU(2) and an SU(3) Yang-Mills theory being in its confining (center) phase. This phase is associated with a dynamical breaking of the local magnetic center…
We study the confinement-deconfinement phase transition of pure Yang-Mills theories at finite temperature using a simple massive extension of standard background field methods. We generalize our recent next-to-leading-order perturbative…
Recent lattice calculations performed at zero temperature and in the maximal center gauge indicate that quark confinement can be understood in this gauge as due to fluctuations in the number of magnetic vortices piercing a given Wilson…
In this paper, we show the existence of magnetic monopoles in the pure $SU(2)$ Yang--Mills theory even in absence of scalar fields when the gauge-invariant mass term is introduced. This result follows from the recent proposal for obtaining…