Casimir force due to condensed vortices in a plane

TL;DR

This paper calculates the Casimir force between parallel lines in a condensed vortex phase of a planar system, using duality to relate a Chern-Simons-Higgs model to a simpler scalar field model, with potential experimental implications.

Contribution

It introduces a novel approach to compute the Casimir force in vortex-condensed phases via duality and scalar field mapping, providing new insights into vortex-related Casimir effects.

Findings

Casimir force can be derived from a dual scalar field model

Boundary conditions significantly affect the Casimir force calculation

Results have potential experimental relevance for vortex systems

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 non-interacting massive scalar fields from which the Casimir force can readily be obtained. The choice of boundary conditions required for the mapped scalar fields and their association with those for the vectorial field and the issues involved are discussed. We also briefly discuss the implications of our results for experiments related to the Casimir effect when vortices can be present.