Instantons and monopoles
Abstract
This study is part of a research program aimed to investigate the relations between instantons, monopoles, and chiral symmetry breaking. Monopoles are important threedimensional topological configurations existing in QCD, which are believed to produce color confinement. Instantons are fourdimensional 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 monopoleantimonopole 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 monopoleantimonopole pair of magnetic charge one adds one zero mode of chirality ±1 , i.e. one instanton of topological charge ±1 .
 Publication:

Physical Review D
 Pub Date:
 March 2015
 DOI:
 10.1103/PhysRevD.91.054512
 arXiv:
 arXiv:1501.06517
 Bibcode:
 2015PhRvD..91e4512D
 Keywords:

 11.15.Ha;
 11.30.Rd;
 12.38.Gc;
 14.80.Hv;
 Lattice gauge theory;
 Chiral symmetries;
 Lattice QCD calculations;
 Magnetic monopoles;
 High Energy Physics  Lattice;
 High Energy Physics  Phenomenology;
 High Energy Physics  Theory;
 Nuclear Theory
 EPrint:
 arXiv admin note: substantial text overlap with arXiv:1412.2704