Magnetic monopole loop for the Yang-Mills instanton

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 ${O(R}^4\ln R)$. We argue that loops will form, in the semiclassical 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 semiclassical precursor to the confinement mechanism.