Abelian dominance for confinement and random phase property of off-diagonal gluons in the maximally abelian gauge Original Research Article

We study abelian dominance for confinement in terms of the local gluon properties in the maximally abelian (MA) gauge both in the analytical consideration and in the lattice QCD. In the MA gauge, the off-diagonal gluon amplitude |Aμ±| is strongly suppressed, which is observed as “microscopic abelian tendency” on the link variable in lattice QCD. According to the suppression of the off-diagonal gluon amplitude, the phase variable of the off-diagonal gluon tends to be random in the MA gauge, besides the residual gauge degrees of freedom. Within the random-variable approximation for the off-diagonal phase variable, we demonstrate that the off-diagonal gluon contribution to the Wilson loop obeys the perimeter law in the MA gauge, and show exact abelian dominance for the string tension, although a small deviation is brought about by the finite size effect of the Wilson loop. We numerically confirm these results using the lattice QCD simulations.