Hopf defects as seeds for monopole loops

TL;DR

This paper analytically explores how instantons in the Laplacian Abelian Gauge can generate monopole loops, revealing that symmetry-breaking perturbations transform pointlike defects into twisted monopole loops with unit charge.

Contribution

It demonstrates that generic instanton configurations produce monopole loops with specific topological properties, extending understanding of instanton-monopole relations in gauge theories.

Findings

Instantons lead to pointlike defects with Hopf invariant one.

Symmetry-breaking perturbations turn these defects into monopole loops.

Monopoles are twisted to reflect the instanton number.

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.