Instanton, Monopole and Confinement

We study the correlation between instantons and QCD-monopoles both in the lattice gauge theory and in the multi-instanton system using the maximally abelian gauge. First, we find the existence of an almost linear correlation between the total length of monopole trajectories and the total number of pseudoparticles (instantons and anti-instantons) in the ${16}^3\times 4$ SU(2) lattice. Second, we study the features of QCD-monopole in the SU(2) multi-instanton vacuum on the ${16}^4$ lattice as a random ensemble of pseudoparticles. A signal of monopole condensation is found as the clustering of monopole trajectories, when the topological pseudoparticles is sufficiently dense.