Aharonov-Bohm Effect in the Abelian-Projected SU(3)-QCD with $\Theta$-term

By making use of the path-integral duality transformation, string representation of the Abelian-projected SU(3)-QCD with the $\Theta$-term is derived. Besides the short-range (self-)interactions of quarks (which due to the $\Theta$-term acquire a nonvanishing magnetic charge, i.e. become dyons) and electric Abrikosov-Nielsen-Olesen strings, the resulting effective action contains also a long-range topological interaction of dyons with strings. This interaction, which has the form of the 4D Gauss linking number of the trajectory of a dyon with the world-sheet of a closed string, is shown to become nontrivial at $\Theta$ not equal to $3\pi$ times an integer. At these values of $\Theta$, closed electric Abrikosov-Nielsen-Olesen strings in the model under study can be viewed as solenoids scattering dyons, which is the 4D analogue of the Aharonov-Bohm effect.