We study effective mass generation of off-diagonal gluons and infrared Abelian dominance in the maximally Abelian ͑MA͒ gauge. Using SU͑2͒ lattice QCD, we investigate the propagator and the effective mass of the gluon field in the MA gauge with U(1) 3 Landau gauge fixing. The Monte Carlo simulation is performed on the 12 3 ϫ24 lattice with 2.2р␤р2.4, and also on the 16 4 and 20 4 lattices with 2.3р␤р2.4. In the MA gauge, the diagonal gluon component A 3 shows long-range propagation, and infrared Abelian dominance is found for the gluon propagator. In the MA gauge, the off-diagonal gluon component A Ϯ behaves as a massive vector boson with the effective mass M off Ӎ1.2 GeV in the region of rտ0.2 fm, and its propagation is limited within a short range. We conjecture that infrared Abelian dominance can be interpreted as infrared inactivity of the offdiagonal gluon due to its large mass generation induced by the MA gauge fixing. ͓S0556-2821͑99͒05223-6͔

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 identified as monopole condensation at a large scale. To prove monopole condensation, we apply the dual gauge formalism to the monopole part, and derive the inter-monopole potential from the dual Wilson loop in the MA gauge. In the monopole part, which carries the nonperturbative aspects of QCD, the dual gluon mass is evaluated as $m_B \simeq $0.5GeV, which is the evidence of the dual Higgs mechanism by monopole condensation. As for the monopole structure, the large fluctuation of off-diagonal gluons remains around the monopole in the MA gauge, 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.Comment: Invited Lecture presented by H. Suganuma at 1997 Yukawa International Seminar (YKIS'97) on `` Non-Perturbative QCD -Structure of the QCD Vacuum-'', 2-12 December 1997, in Kyoto, Japan, 12 pages, Plain Late

We show the construction of the dual superconducting theory for the confinement mechanism from QCD in the maximally abelian (MA) gauge using the lattice QCD Monte Carlo simulation. We find that essence of infrared abelian dominance is naturally understood with the off-diagonal gluon mass m off ≃ 1.2GeV induced by the MA gauge fixing. In the MA gauge, the off-diagonal gluon amplitude is forced to be small, and the off-diagonal gluon phase tends to be random. As the mathematical origin of abelian dominance for confinement, we demonstrate that the strong randomness of the off-diagonal gluon phase leads to abelian dominance for the string tension. In the MA gauge, there appears the macroscopic network of the monopole world-line covering the whole system. We investigate the monopole-current system in the MA gauge by analyzing the dual gluon field B µ . We evaluate the dual gluon mass as m B = 0.4 ∼ 0.5GeV in the infrared region, which is the lattice-QCD evidence of the dual Higgs mechanism by monopole condensation. Owing to infrared abelian dominance and infrared monopole condensation, QCD in the MA gauge is describable with the dual Ginzburg-Landau theory.

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