Monopole Dominance of Confinement in SU(3) Lattice QCD

To check the dual superconductor picture for the quark-confinement mechanism, we evaluate monopole dominance as well as Abelian dominance of quark confinement for both quark-antiquark and three-quark systems in SU(3) quenched lattice QCD in the maximally Abelian (MA) gauge. First, we examine Abelian dominance for the static $Qbar Q$ system in lattice QCD with various spacing $a$ at $beta$=5.8-6.4 and various size $L^3$x$L_t$. For large physical-volume lattices with $La ge$ 2fm, we find perfect Abelian dominance of the string tension for the $Qbar Q$ systems: $sigma_{Abel} simeq sigma$. Second, we accurately measure the static 3Q potential for more than 300 different patterns of 3Q systems with 1000-2000 gauge configurations using two large physical-volume lattices: ($beta$,$L^3$x$L_t$)=(5.8,$16^3$x32) and (6.0,$20^3$x32). For all the distances, the static 3Q potential is found to be well described by the Y-Ansatz: two-body Coulomb term plus three-body Y-type linear term $sigma L_{min}$, where $L_{min}$ is the minimum flux-tube length connecting the three quarks. We find perfect Abelian dominance of the string tension also for the 3Q systems: $sigma^{Abel}_{3Q}simeq sigma_{3Q} simeq sigma$. Finally, we accurately investigate monopole dominance in SU(3) lattice QCD at $beta$=5.8 on $16^3$x32 with 2,000 gauge configurations. Abelian-projected QCD in the MA gauge has not only the color-electric current $j^mu$ but also the color-magnetic monopole current $k^mu$, which topologically appears. By the Hodge decomposition, the Abelian-projected QCD system can be divided into the monopole part ($k_mu e 0$, $j_mu=0$) and the photon part ($j_mu e 0$, $k_mu=0$). We find monopole dominance of the string tension for $Qbar Q$ and 3Q systems: $sigma_{Mo}simeq 0.92sigma$. While the photon part has almost no confining force, the monopole part almost keeps the confining force.