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We give a definition of gauge-invariant magnetic monopoles in Yang-Millstheory without using the Abelian projection due to 't Hooft. They automaticallyappear from the Wilson loop operator. This is shown by rewriting the Wilsonloop operator using a non-Abelian Stokes theorem. The magnetic monopole definedin this way is a topological object of co-dimension 3, i.e., a loop infour-dimensions. We show that such magnetic loops indeed exist infour-dimensional Yang-Mills theory. In fact, we give an analytical solutionrepresenting circular magnetic monopole loops joining a pair of merons in thefour-dimensional Euclidean SU(2) Yang-Mills theory. This is achieved by solvingthe differential equation for the adjoint color (magnetic monopole) field inthe two--meron background field within the recently developed reformulation ofthe Yang-Mills theory. Our analytical solution corresponds to the numericalsolution found by Montero and Negele on a lattice. This result stronglysuggests that a meron pair is the most relevant quark confiner in the originalYang-Mills theory, as Callan, Dashen and Gross suggested long ago.

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