QCD-monopoles and Instantors for Color Confinement

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This year, I have studied "quark confinement" in quantum chromodynamics (QCD) based on the lattice-QCD Monte Carlo simulations and the QCD effective theory. The main results are listed as follows.1. Using the lattice QCD, I have investigated gluon propagators in the maximally abelian (MA) gauge, and have shown that the off-diagonal gluon behaves as a massive field with a large mass about 1 GeV in the MA gauge. Such effective mass generation of off-diagonal gluons is considered as the physical origin of "abelian dominance" for the nonperturbative QCD, which has been observed in the lattice QCD.2. I have pointed out the strong randomness of the off-diagonal gluon phase in the MA gauge, due to the strong suppression of the off-diagonal gluon amplitude. I have also analytically proved perfect "abelian dominance" for the string tension or the confinement force, within the random-variable approximation for the off-diagonal gluon phase.3. From the mathematical analysis on the MA gauge fixing, I have derived the SU(NィイD2cィエD2) gauge-invariance criterion for the physical quantities defined in the MA gauge.4. I have found that the QCD-monopole, which appears in the MA gauge, has a peculiar structure relating to the large off-diagonal gluon amplitude around its center like the't Hooft-Polyakov monopole.5. I have investigated the glueball as a color-flux ring. I have also estimated the decay rate of the 0ィイD1++ィエD1-scalar glueball which is identified as QCD-monopole (the dual Higgs particle).6. I have shown extended-monopole clustering in the multi-instanton system in the MA gauge. I have also found the confining force arising in the intermediate range about 1 fm in the multi-instanton system.7. I have predicted a local correlation between instantons and QCD-monopoles in the MA gauge in terms of the off-diagonal gluon.