The dual Ginzburg-Landau theory for confinement and the role of instantons

We review the dual Ginzburg-Landau (DGL) theory, in which color monopoles and their condensation in the QCD vacuum play the essential role for confinement and chiral symmetry breaking. The color monopoles live, however, only in a particular gauge, the maximal abelian gauge. Hence, we discuss next the origin of the color monopole, which we conjecture is instanton, the classical solution of the Euclidean Yang-Mills theory. We make one to one correspondence of instanton and color monopole and further of instanton and center vortex. We then study the appearance of monopole condensation due to large density of instantons in the model QCD vacuum. Instantons are found the key objects to provide not only chiral symmetry breaking, but also quark confinement. We should further take into account the correlations among instantons for quantitative description of confinement. (author)