Vortex condensation in the Chern-Simons Higgs model: An existence theorem
type: Item
instance of: scholarly article
title: Vortex condensation in the Chern-Simons Higgs model: An existence theorem
zbMATH Open document ID: 0846.58063
DOI: 10.1007/BF02101552
author: Luis Caffarelli
author: Yisong Yang
published in: Communications in Mathematical Physics
publication date: 1995-08-03T00:00:00Z
review text: The authors discuss the self-dual model of the Chern-Simons Higgs theory on a \((2 + 1)\)-dimensional Minkowski spacetime. This is a special case of the anyon model. They study stationary solutions over a periodic cell with specific gauge-periodic boundary conditions and prove that there exists a critical value \(\kappa_c\) of the Chern-Simons coupling parameter \(\kappa\) so that for models with \(\kappa < \kappa_c\) admit self-dual doubly periodic vortex solutions. In models with \(\kappa > \kappa_c\) the vortex solutions are absent. An alternative variational approach to the problem is also discussed.
Mathematics Subject Classification ID: 58Z05
Mathematics Subject Classification ID: 81T10
Mathematics Subject Classification ID: 83C47
zbMATH DE Number: 778962
zbMATH Keywords: self-dual model
zbMATH Keywords: Chern-Simons Higgs theory
zbMATH Keywords: Minkowski spacetime
zbMATH Keywords: anyon model
zbMATH Keywords: Chern-Simons coupling parameter
zbMATH Keywords: vortex solutions
reviewed by: Kishore Marathe
MaRDI profile type: Publication
cites work: Meilleures constantes dans le théorème d'inclusion de Sobolev et un théorème de Fredholm non linéaire pour la transformation conforme de la courbure scalaire
cites work: Conformal complete metrics with prescribed non-negative Gaussian curvature in \({\mathbb{R}}^ 2\)
cites work: Prescribing Gaussian curvature on S 2
cites work: A nonlinear elliptic equation arising from gauge field theory and cosmology
cites work: Bosonization, topological solitons and fractional charges in two- dimensional quantum field theory
cites work: Quantum field theories of vortices and anyons
cites work: Multivortex solutions of the Abelian Chern-Simons-Higgs theory
cites work: Self-dual Chern-Simons vortices
cites work: Integrability conditions for $\Delta u = k - Ke^{\alpha u}$ with applications to Riemannian geometry
cites work: Curvature functions for compact 2-manifolds
cites work: Curvature functions for open 2-manifolds
cites work: Q3336320
cites work: On the elliptic equation \(\Delta \omega + K(x)e^{2\omega} = 0\) and conformal metrics with prescribed Gaussian curvatures
cites work: Abelian Chern-Simons theories in \(2+1\) dimensions
cites work: The existence of non-topological solitons in the self-dual Chern-Simons theory
cites work: Arbitrary N-vortex solutions to the first order Ginzburg-Landau equations
cites work: On the equivalence of the first and second order equations for gauge theories
cites work: Abrikosov’s Vortices in the Critical Coupling
full work available at URL: https://doi.org/10.1007/bf02101552
OpenAlex ID: W1983558565
Recommended article: Vortex condensation in the dual Chern-Simons-Higgs model
Recommended article: Vortex condensation in \({U(1)\times U(1)}\) Chern-Simons model with a general Higgs potential on a torus
Recommended article: Vortex condensates for the SU(3) Chern-Simons theory
Recommended article: Vortex-condensations of a non-relativistic Maxwell-Chern-Simons theory
Recommended article: Asymptotics for the vortex condensate solutions in Chern-Simons-Higgs theory
Recommended article: Existence theorems for non-abelian Chern-Simons-Higgs vortices with flavor
Recommended article: The existence of Chern-Simons vortices
Recommended article: Vortex condensation in general \(U(1) \times U(1)\) abelian Chern-Simons model on a flat torus
Recommended article: Double vortex condensates in the Chern-Simons-Higgs theory
description: scientific article; zbMATH DE number 778962