Confinement Physics and Topology in QCD

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 physics is interpreted as the effective mass $m_{ch} \simeq 0.9 {\rm GeV}$ of the charged gluon 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. Using the dual Wilson loop in the MA gauge, we find the effective mass of the dual gluon field, $m_B \simeq $0.5GeV, which is the evidence of the dual Higgs mechanism by monopole condensation. The large fluctuation of off-diagonal gluons remains around the monopole in the MA gauge, and this charged-gluon rich region 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.