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Representations of the Abelian-projected SU(2)- and SU(3)-gluodynamics interms of the magnetic monopole currents are derived. Besides the quadraticpart, the obtained effective actions contain interactions of these currentswith the world-sheets of electric strings in 4D or electric vortex lines in 3D.Next, we illustrate that 3D compact QED is a small gauge boson mass limit of 3DAbelian Higgs model with external monopoles and give a physical interpretationto the confining string theory as the integral over the monopole densities.Finally, we derive the bilocal field strength correlator in the weak-fieldlimit of 3D compact QED, which turns out to be in line with the one predictedby the Stochastic Vacuum Model.Comment: 18 pages, LaTeX2e, no figure

Confining properties of Abelian-projected theories