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 ± µ acquires the effective mass as M off ≃ 1.2 GeV. From the monopole current in the MA gauge, we extract the dual gluon field B µ and estimate the dual gluon mass as m B ≃ 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. Strong Randomness of Off-diagonal Gluon Phase in MA gaugeWe find strong randomness of the off-diagonal gluon phase χ µ in the MA gauge using the SU(2) lattice QCD [1,2]. In fact, we find very small correlation between neighboring phases, χ µ (s) and χ µ (s+ν), on the lattice in the MA and U(1) 3 Landau gauge. This tendency seems natural because of the following reasons. Off-diagonal gluon phase χ µ is not constrained by the MA gauge-fixing condition at all, and the constraint from the QCD action is also small because of strong suppression of the off-diagonal gluon amplitude |A ± µ | in the MA gauge. Within the random phase-variable approximation, perfect abelian dominance for the string tension can be clearly demonstrated [1,2]. Propagator and Effective Mass of Off-diagonal Gluon in MA gaugeUsing the SU(2) lattice QCD with 12 3 ×24, 16 4 and 20 4 , we study the off-diagonal gluon propagator G off µµ (r) ≡ A + µ (x)A − µ (y) as the function of r ≡ (x − y) 2 in the MA gauge with U(1) 3 Landau gauge fixing [2,3]. From the slope of the logarithmic plot of r 3/2 G off µµ (r) in Fig.1(a), we get the off-diagonal gluon mass as M off ≃ 1.2 GeV in the MA gauge [2,3] as shown in Fig.1(b). Thus, in the MA gauge, the off-diagonal gluon cannot carry the long-range interaction such as the con- * finement force. This is the essence of infrared abelian dominance. In fact, QCD in the MA gauge behaves as a strong-coupling compact QED at the larger scale than M −1 off ≃ 0.2 fm [2,3]. 0.001 0.01 0.1 1 r 3/2 G µµ (r) 1.2 1.0 0.8 0.6 0.4 0.2 r [fm] r 3/2 G µµ off (r) r 3/2 G µµ Abel (r) 12 3 X 24,16 4 ,20 4 [GeV 1/2 ] Abel off β ---
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