This paper explores long-range interactions between magnetically-charged excitations of the vacuum of the dual Landau-Ginzburg theory (DLGT) and the dual Abrikosov vortices present in the same vacuum. We show that, in the London limit of DLGT, the corresponding Aharonov-Bohm-type interactions possess such a coupling that the interactions reduce to a trivial factor of e^{2pi i (integer)}. The same analysis is done in the SU(N_c)-inspired [U(1)]^{N_c-1}-invariant DLGT, as well as in DLGT extended by a Chern-Simons term. It is furthermore explicitly shown that the Chern-Simons term leads to the appearance of knotted dual Abrikosov vortices.
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