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.

arXiv comment29 (cover + 28) pages, 3 figures; references are added, minor changes, version accepted for publication in Physical Review D,

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• Jackiw-Nohl-Rebbi two-instanton as a source of magnetic monopole loop
• Vacuum structure and string tension in Yang-Mills dimeron ensembles
• Color confinement and restoration of residual local gauge symmetries