Confining properties of Abelian-projected theories

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 four dimensions (4D) or electric vortex lines in three dimensions (3D). Next, Re illustrate that 3D compact QED is a small gauge-boson mass limit of a 3D Abelian Higgs model with external monopoles and give a physical interpretation of 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.