Monopole Dominance for Nonperturbative QCD

Monopole dominance for the nonperturbative features in QCD is studied both in the continuum and the lattice gauge theories. First, we study the dynamical chiral-symmetry breaking (D$\chi$SB) in the dual Higgs theory using the effective potential formalism. We find that the main driving force for D$\chi$SB is brought from the confinement part in the nonperturbative gluon propagator rather than the short-range part, which means monopole dominance for D$\chi$SB. Second, the correlation between instantons and QCD-monopoles is studied. In the Polyakov-like gauge, where $A_4(x)$ is diagonalized, the QCD-monopole trajectory penetrates the center of each instanton, and becomes complicated in the multi-instanton system. Finally, using the SU(2) lattice gauge theory with $16^4$ and $16^3 \times 4$, the instanton number is measured in the singular (monopole-dominating) and regular (photon-dominating) sectors, respectively. Instantons and anti-instantons only exist in the monopole sector both in the maximally abelian gauge and in the Polyakov gauge, which means monopole dominance for the topological charge.Comment: Talk presented by H. Suganuma at the Joint Japan-Australia Workshop on "Quarks, Hadrons and Nuclei'', 15 - 24 Nov. 1995, in Adelaide, Australia, 10 pages, Plain Latex, ( 6 figures - available on request from [email protected]