Magnetic monopole loop for the Yang-Mills instanton

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.