Instantons and monopoles

This study is part of a research program aimed to investigate the relations between instantons, monopoles, and chiral symmetry breaking. Monopoles are important three-dimensional topological configurations existing in QCD, which are believed to produce color confinement. Instantons are four-dimensional topological configurations and are known to be related to chiral symmetry breaking. To study the relation between monopoles and instantons we generate configurations which add static monopole-antimonopole pairs of opposite charges to the vacuum state by use of a monopole creation operator. We observe that the monopole creation operator only adds long monopole loops to the configurations. We then count the number of fermion zero modes using overlap fermions as a tool. As a result we find that each monopole-antimonopole pair of magnetic charge one adds one zero mode of chirality +/- 1, i.e. one instanton of topological charge +/- 1.