SU(2) Chern-Simons Theory Coupled to Competing Scalars

TL;DR

This paper investigates vortex solutions in a SU(2) Chern-Simons-Higgs model coupled to a competing scalar, revealing how different parameter regimes affect vortex structure and connecting these findings to high-temperature superconductor phenomena.

Contribution

It introduces a novel analysis of vortex solutions in a coupled SU(2) Chern-Simons-Higgs model with a competing scalar field, including the derivation of the low-energy moduli theory.

Findings

Vortex solutions with halo structures depending on scalar couplings.

Existence of parameter regions with no vortex solutions.

Connection to competing orders in high-temperature superconductors.

Abstract

We study a spontaneously broken SU(2) Chern-Simons-Higgs model coupled though a Higgs portal to an uncharged triplet scalar with a vacuum state competing with the Higgs one. We find vortex-like solutions to the field equations in different parameter space regions. Depending on the scalar coupling constants we find a parameter region in which the competing order creates a halo about the Chern-Simons-Higgs vortex core, together with two other regions, one where no vortex solutions exist, the other where ordinary Chern-Simons-Higgs vortices can be found. We derive the low-energy theory for the moduli fields on the vortex world sheet and also discuss the connection of our results with those found in studies of competing orders in high temperature superconductors.