Existence of Chiral-Asymmetric Zero Modes in the Background of QCD-Monopoles

There are two distinct pictures of the vacuum structure in QCD. One is based on the appearance of color-magnetic monopoles (QCDmonopoles) after performing the abelian gauge xing [1]. The recent lattice QCD simulations show that the dual Meissner e ect brought to the QCD vacuum by QCD-monopole condensation [2]. Hence, color con nement could be regarded as the dual version of the superconductivity. On the other hand, QCD has also classical and non-trivial gauge con gurations (instantons) as topological defects in the Euclidean 4-space. As well known, the instanton liquid characterized by a random ensemble of instantons and antiinstanton succeeds in explaining several properties of light hadrons, e.g. spontaneous chiralsymmetry breaking (S SB) [3]. It seems that QCD-monopoles and instantons are relevant topological objects for the description of each phenomenon. Here, we should mention that QCD-monopoles would play an essential role on non-perturbative features of QCD, which includes S SB. This possibility was studied by using the Schwinger-Dyson equation with the gluon propagator in the background of condensed monopoles [4]. The idea of providing S SB due to QCD-monopole condensation was supported by the lattice simulations [5,6]. Thus, these results