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We investigate the Maximally Abelian (MA) Projection for a single $SU(2)$ instanton in continuum gauge theory. We find that there is a class of solutions to the differential MA gauge condition with circular monopole loops of radius $R$ centered on the instanton of width $rho$. However, the MA gauge fixing functional $G$ decreases monotonically as $R/rho rightarrow 0$. Its global minimum is the instanton in the singular gauge. We point out that interactions with nearby anti-instantons are likely to excite these monopole loops.
The confinement scenario in Maximally Abelian gauge (MAG) is based on the concepts of Abelian dominance and of dual superconductivity. Recently, several groups pointed out the possible existence in MAG of ghost and gluon condensates with mass dimensi
We study decomposition of $SU(2)$ gauge field into monopole and monopoleless components. After fixing the Maximal Abelian gauge in $SU(2)$ lattice gauge theory we decompose the nonabelian gauge field into the Abelian field created by monopoles and th
We perform the Monte Carlo study of the SU(3) non-Abelian Higgs model. We discuss phase structure and non-Abelian vortices by gauge invariant operators. External magnetic fields induce non-Abelian vortices in the color-flavor locked phase. The spatia
The effects of the Gribov copies on the gluon and ghost propagators are investigated in SU(2) Euclidean Yang-Mills theory quantized in the maximal Abelian gauge. By following Gribovs original approach, extended to the maximal Abelian gauge, we are ab
We perform various lattice numerical analyses with the energy-momentum tensor (EMT) defined through the gradient flow. We explore the spatial distribution of the stress tensor in static quark-anti-quark systems and thermodynamic quantities at nonzero