Vortex Condensation in the Dual Chern-Simons Higgs Model

TL;DR

This paper investigates vortex excitations in the self-dual Chern-Simons-Higgs model, using duality to analyze vortex condensation and critical parameters, including quantum corrections, to understand phase transitions.

Contribution

It introduces a dual field theory for vortices in the Chern-Simons-Higgs model and identifies the critical Chern-Simons parameter for vortex condensation.

Findings

Vortex degrees of freedom are explicitly coupled to a dual gauge field.

A critical value for the Chern-Simons parameter is determined for vortex condensation.

Quantum self-energy corrections to vortices are analyzed.

Abstract

The contribution of nontrivial vacuum (topological) excitations, more specifically vortex configurations of the self-dual Chern-Simons-Higgs model, to the functional partition function is considered. By using a duality transformation, we arrive at a representation of the partition function in terms of which explicit vortex degrees of freedom are coupled to a dual gauge field. By matching the obtained action to a field theory for the vortices, the physical properties of the model in the presence of vortex excitations are then studied. In terms of this field theory for vortices in the self-dual Chern-Simons Higgs model, we determine the location of the critical value for the Chern-Simons parameter below which vortex condensation can happen in the system. The effects of self-energy quantum corrections to the vortex field are also considered.