Magnetic monopole loops supported by a meron pair as the quark confiner

Abstract

We give an analytical solution representing circular magnetic monopole loops joining a pair of merons in the four-dimensional Euclidean SU(2) Yang-Mills theory. This is achieved by solving the differential equation for the adjoint color (magnetic monopole) field in the two-meron background field within the recently developed reformulation of the Yang-Mills theory. Our analytical solution corresponds to the numerical solution found by Montero and Negele on a lattice. This result strongly suggests that a meron pair is the most relevant quark confiner in the original Yang-Mills theory, as Callan, Dashen, and Gross suggested long ago.