Instantons and Monopoles in the Nonperturbative QCD

Abstract

On the basis of the dual-superconductor picture, we study the confinement physics in QCD in terms of the topological objects as monopoles in the maximally abelian (MA) gauge using the SU(2) lattice QCD. In the :'viA 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 /3. By regarding the angle variable in the off­ diagonal factor as a random variable, we derive the analytical formula of the off-diagonal gluon contribution Wctr to the Wilson loop in relation with the microscopic variable of the diagonal gluon component in the MA gauge. We find that Wcff obeys the perimeter law, which leads to abelian dominance on the string tension. To clarify the origin of abelian dominance for the long-range physics, we study the charged-gluon propagator in the MA gauge using the lattice QCD, and find that the effective mass mch :::::: 0.9 GeV of the charged gluon is induced by the MA gauge fixing. In the MA gauge, there appears the macroscopic network of the monopole world-line covering the whole system, which would be identified as monopole condensation at a large scale. To prove monopole condensation in the field­ theoretical manner, we apply the dual gauge formalism to the monopole part, and derive the inter-monopole potential from the dual \Nilson loop in the MA gauge. In the monopole part, which carries the nonperturbative aspects of QCD, the dual gluon mass is evaluated as mD ::::::0.5 GeV in the infrared region, which is the evidence of the dual Higgs mechanism by monopole condensation. We study the action density around the QCD-monopole in the MA gauge. Around the monopole in the MA gauge, there remains the large fluctuation of off­ diagonal gluons, and large cancellation occurs between the diagonal and off-diagonal action densities to keep the total QCD action finite. The charged-gluon rich region around the QCD-monopole would provide the effective monopole size as the critical scale of the abelian projected QCD. Instantons are expected to appear in the charged-gluon rich region around the monopole world-line in the MA gauge, which leads to the local correlation between monopoles and instantons. §1. Dual superconductor picture for confinement in QCD Quantum Chromodynamics (QCD) shows the asymptotic freedom due to its nonabelian nature, and the perturbative calculation is workable in the ultraviolet region as J1. » 1 GeV. On the other hand, in the infrared region as J1. :S 1 GeV, QCD exhibits nonperturbative phenomena like color confinement arid dynamical chiral­ symmetry breaking (DxSB) due to the strong-coupling nature. Up to now, there is no systematic promising method for the study of the nonperturbative QCD (NP­ QCD) except for the lattice QCD calculation with the Monte Carlo method. The lattice QCD simulation can be regarded as a numerical experiment based on the rigid field-theoretical framework, and provides a powerful technique for the analyses of the NP-QCD vacuum and hadrons. Owing to the great progress of the computer power in these days, the lattice QCD becomes useful not only for reproductions of hadron properties but also for new predictions like glueball