  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^{2\pi 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.
