Infrared Abelian Dominance and Dual Higgs Mechanism in MA Gauge

Abstract

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 ---