April 17, 1998
We study the nonperturbative QCD in terms of topological objects, i.e., QCD-monopoles and instantons. In the 't Hooft abelian gauge, QCD is reduced into an abelian gauge theory with QCD-monopoles, and the confinement mechanism can be understood with the dual superconductor picture. Regarding the flux-tube ring as the glueball, we study the glueball properties by combining the dual Ginzburg-Landau theory and the Nambu-Goto action. We find the strong correlations between instantons and monopole world-lines both in the continuum theory and in the lattice QCD. The nonperturbative QCD vacuum is filled with instantons and monopoles, and dense instantons generate a macroscopic network of the monopole world-line, which would be responsible for the confinement force in the infrared region.
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October 13, 1997
The confinement mechanism in the nonperturbative QCD is studied in terms of topological excitation as QCD-monopoles and instantons. In the 't Hooft abelian gauge, QCD is reduced into an abelian gauge theory with monopoles, and the QCD vacuum can be regarded as the dual superconductor with monopole condensation, which leads to the dual Higgs mechanism. The monopole-current theory extracted from QCD is found to have essential features of confinement. We find also close relation...
April 20, 1998
We study the confinement physics in QCD in the maximally abelian (MA) gauge using the SU(2) lattice QCD. To clarify the origin of abelian dominance for the long-range physics, we study the charged-gluon propagator in the lattice QCD, and find that the effective mass $m_{ch} \simeq 0.9 {\rm GeV}$ of the charged gluon is induced by the MA gauge fixing. In the MA gauge, there appears the global network of the monopole world-line covering the whole system, which would be identifi...
April 17, 1998
Based on the dual-superconductor picture, we study the confinement physics in QCD in terms of the monopole in the maximally abelian (MA) gauge using the SU(2) lattice QCD. In the MA gauge, the off-diagonal gluon component is forced to be small, and hence microscopic abelian dominance on the link variable is observed in the lattice QCD for the whole region of $\beta$. From the gluon-propagator analysis in the lattice QCD, the origin of abelian dominance for the long-range phys...
September 18, 1996
We study the relation between instantons and monopoles in the abelian gauge. First, we investigate the monopole in the multi-instanton solution in the continuum Yang-Mills theory using the Polyakov gauge. At a large instanton density, the monopole trajectory becomes highly complicated, which can be regarded as a signal of monopole condensation. Second, we study instantons and monopoles in the SU(2) lattice gauge theory both in the maximally abelian (MA) gauge and in the Polya...
October 25, 2000
We review the physics of topological objects in QCD. Topics include: solitons, vortices, magnetic monopoles, instantons, (effective theories of) confinement.
September 28, 1996
We study the correlation between instantons and QCD-monopoles both in the lattice gauge theory and in the multi-instanton system using the maximally abelian gauge. First, we find the existence of an almost linear correlation between the total length of monopole trajectories and the total number of pseudoparticles (instantons and anti-instantons) in the $16^{3}\times4$ SU(2) lattice. Second, we study the features of QCD-monopole in the SU(2) multi-instanton vacuum on the $16^{...
September 13, 1995
We review recent results from lattice on topological aspects of QCD: most of the results refer to monopoles and to instantons. We discuss in detail the evidence for condensation of monopoles in the vacuum and confinement of colour by dual superconductivity, and the major role of monopoles in dynamics (monopole dominance). As for instantons we review the $U(1)$ problem, a possible determination of the spin content of the proton, and new lattice data relevant to instanton liqui...
February 6, 1997
We analyze the interplay of topological objects in four-dimensional QCD on the lattice. The distributions of color magnetic monopoles in the maximum abelian gauge are computed around instantons in both pure and full QCD. We find an enhanced probability for monopoles inside the core of an instanton on gauge field average. This feature is independent of the topological charge definition used. For specific gauge field configurations we visualize the situation graphically. Moreov...
December 19, 1995
The correlation between instantons and QCD-monopoles is studied both in the lattice gauge theory and in the continuum theory. From a simple topological consideration, instantons are expected to live only around the QCD-monopole trajectory in the abelian gauge. First, the instanton solution is analytically studied in the Polyakov-like gauge, where $A_4(x)$ is diagonalized. The world line of the QCD-monopole is found to be penetrate the center of each instanton inevitably. For ...
February 22, 1996
Monopole dominance for the nonperturbative features in QCD is studied both in the continuum and the lattice gauge theories. First, we study the dynamical chiral-symmetry breaking (D$\chi $SB) in the dual Higgs theory using the effective potential formalism. We find that the main driving force for D$\chi $SB is brought from the confinement part in the nonperturbative gluon propagator rather than the short-range part, which means monopole dominance for D$\chi $SB. Second, the c...