Infrared Abelian Dominance and Dual Higgs Mechanism in Maximally Abelian Gauge

We study infrared abelian dominance and the dual Higgs mechanism in the maximally abelian (MA) gauge using the lattice QCD Monte Carlo simulation. In the MA gauge, the off-diagonal gluon phase tends to be random, and the off-diagonal gluon $A_\mu^\pm$ acquires the effective mass as $M_{\rm off} \simeq$ 1.2 GeV. From the monopole current in the MA gauge, we extract the dual gluon field $B_\mu$ and estimate the dual gluon mass as $m_B \simeq $ 0.5 GeV. The QCD-monopole structure is also investigated in terms of off-diagonal gluons. From the lattice QCD in the MA gauge, the dual Ginzburg-Landau (DGL) theory can be constructed as a realistic infrared effective theory based on QCD.