Abstract
The Casimir force between parallel lines in a theory describing condensed vortices in a plane is determined. We make use of the relation between a Chern-Simons-Higgs model and its dualized version, which is expressed in terms of a dual gauge field and a vortex field. The dual model can have a phase of condensed vortices, and, in this phase, there is a mapping to a model of two noninteracting massive scalar fields from which the Casimir force is readily obtained. We also discuss the details concerning the boundary conditions required for the scalar fields and their association with those for the vectorial field. We show that this association is subtle for the case of the transformations considered.
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