The role of monopoles for color confinement

We study the role of the monopole for color confinement by using the monopole current system. For the self-energy of the monopole current less than ln(2d - 1), long and complicated monopole world-lines appear and the Wilson loop obeys the area law, and therefore the monopole current system almost reproduces essential features of confinement properties in the long-distance physics. In the short-distance physics, however, the monopole-current theory would become nonlocal due to the monopole size effect. This monopole size would provide a critical scale of QCD in terms of the dual Higgs mechanism. (orig.)