Aharonov–Bohm effect in the Abelian-projected SU(3)-QCD with Θ-term

By making use of the path-integral duality transformation, string representation of the Abelian-projected SU(3)-QCD with the Θ-term is derived. Besides the short-range (self-)interactions of quarks (which due to the Θ-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 Θ≠3π× integer. At these values of Θ, 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.