Triviality of the Aharonov-Bohm interaction in a spatially confining vacuum

TL;DR

This paper demonstrates that in a confining vacuum, Aharonov-Bohm interactions between magnetic excitations and vortices are trivial, with extensions showing knotted vortices due to Chern-Simons terms.

Contribution

It shows the triviality of Aharonov-Bohm interactions in a confining vacuum and explores effects of Chern-Simons terms on vortex topology.

Findings

Aharonov-Bohm interactions reduce to trivial factors e^{2\pi i (integer)}.

Chern-Simons terms induce knotted dual Abrikosov vortices.

Interaction analysis is performed in various dual Landau-Ginzburg theories.

Abstract

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.