  Representations of the Abelian-projected SU(2)- and SU(3)-gluodynamics in
terms of the magnetic monopole currents are derived. Besides the quadratic
part, the obtained effective actions contain interactions of these currents
with 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 3D
Abelian Higgs model with external monopoles and give a physical interpretation
to the confining string theory as the integral over the monopole densities.
Finally, we derive the bilocal field strength correlator in the weak-field
limit of 3D compact QED, which turns out to be in line with the one predicted
by the Stochastic Vacuum Model.
