Zero modes, Instantons, and Monopoles

Abstract: The purpose of this study is to show the relations between monopoles instantons and Chiral symmetry breaking. First, in order to show the relation between instantons and monopoles, we generate configurations, adding monopoles by a monopole creation operator. Then, we count the number of fermion zero modes in the configurations using Overlap fermions as a tool. As a result we find that one monopole with plus one charge and one anti-monopole with minus one charge make one instanton of charge plus or minus one. We have already reported these results elsewhere. In addition, in this report, the relation between the additional monopoles and Chiral symmetry breaking is discussed. We compute the Chiral condensate, the pseudo-scalar mass, and the pion decay constant. Preliminary results show that the additional monopoles do affect Chiral symmetry breaking.