Hopf defects as seeds for monopole loops

Abstract

We investigate the relation between instantons and monopoles in the Laplacian Abelian Gauge using analytical methods in the continuum. Our starting point is the fact that the 't Hooft instanton with its high symmetry leads to a pointlike defect with Hopf invariant one. In order to generalise this result we partly break the symmetry by a local perturbation. We find that for generic configurations near the 't Hooft instanton the defects become loops. The analytical results show explicitly that these defects are magnetic monopoles with unit charge. In addition, the monopoles are twisted to account for the instanton number of the background.

latex, 6 pages, 2 figures; v2: references added, emphasis modified, conclusions unchanged

References in corpus (7)

• Center Vortices and Monopoles without lattice Gribov copies
• The relevance of center vortices
• Instantons and Gribov Copies in the Maximally Abelian Gauge
• Instantons and Monopoles in General Abelian Gauges
• Magnetic monopoles vs. Hopf defects in the Laplacian (Abelian) gauge
• Abelian and center gauges in continuum Yang-Mills-Theory
• Overlapping Instantons

Cited by in corpus (3)

• Writhe of center vortices and topological charge -- an explicit example
• Magnetic Monopole Loops supported by a Meron pair as the Quark Confiner
• Jackiw-Nohl-Rebbi two-instanton as a source of magnetic monopole loop