Zero modes of Overlap fermions, instantons, and monopoles

The purpose of this study is to investigate the relations between instantons, monopoles, and Chiral symmetry breaking. The monopoles are important topological configurations existing in QCD which are believed to produce colour confinement. The groups of University of Kanazawa and Pisa have produced by Lattice simulations many results supporting the idea that QCD vacuum is a dual superconductor. Instantons are related to Chiral symmetry breaking, as explained e.g. in the instanton liquid model of E. V. SHURYAK. Clarifying quantitatively the relation between monopoles and instantons is not easy, also because monopoles are three dimensional objects, while instantons are four dimensional. We generate configurations, adding monopole-antimonopole pairs of opposite charges by a monopole creation operator. We observe that the monopole creation operator only adds long monopole loops in the configurations. Then, we count the number of fermion zero modes in the configurations using Overlap fermions as a tool. Finally, we find that one monopole-antimonopole pair makes one zero mode of plus or minus chirality, that is to say, one instanton of plus or minus charge.