Monopole Dominance for Nonperturbative QCD

Abstract

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.