Magnetic monopole loop for the Yang-Mills instanton

TL;DR

This paper explores how monopole loops associated with instantons in QCD could form and percolate, potentially serving as a semi-classical precursor to quark confinement.

Contribution

It identifies a circular monopole trajectory around an instanton and discusses conditions under which monopole loops form and percolate, linking to confinement.

Findings

Monopole loops are circular with a radius centered on the instanton.

Loop formation is marginally stable at zero radius, with perturbations promoting formation.

Percolation of monopole loops may signal confinement in the semi-classical limit.

Abstract

We investigate 't Hooft-Mandelstam monopoles in QCD in the presence of a single classical instanton configuration. The solution to the Maximal Abelian projection is found to be a circular monopole trajectory with radius $R$ centered on the instanton. At zero loop radius, there is a marginally stable (or flat) direction for loop formation to $O(R^4 logR)$. We argue that loops will form, in the semi-classical limit, due to small perturbations such as the dipole interaction between instanton anti-instanton pairs. As the instanton gas becomes a liquid, the percolation of the monopole loops may therefore provide a semi-classical precursor to the confinement mechanism.