Zero modes of the non-relativistic self-dual Chern-Simons vortices on the Toda backgrounds
type: Item
instance of: scholarly article
title: Zero modes of the non-relativistic self-dual Chern-Simons vortices on the Toda backgrounds
zbMATH Open document ID: 0732.35076
DOI: 10.1016/0003-4916(91)90208-P
author: Yongsung Yoon
published in: Annals of Physics
publication date: 1991-01-01T00:00:00Z
review text: The two-dimensional self-dual equations are the governing equations of the static zero-energy vortex solutions for the non-relativistic, non- Abelian Chern-Simons models. The zero modes of the non-relativistic vortices are examined by index calculation for the self-dual equations. The index for the self-dual equations is zero for non-Abelian groups, but a non-zero index is obtained by the Toda Ansatz which reduces the self- dual equations to the Toda equations. The number of zero modes for the non-relativistic Toda vortices is \(2\sum^{r}_{\alpha,\beta}K_{\alpha \beta}Q^{\beta}\) which is twice the total number of isolated zeroes of the vortex functions. For the affine Toda system, there are additional adjoint zero modes which give a zero index for the SU(N) group.
Mathematics Subject Classification ID: 35Q40
Mathematics Subject Classification ID: 81R10
zbMATH DE Number: 4210686
reviewed by: Yeon Soo Yoon
MaRDI profile type: Publication
cites work: Hierarchy of soliton solutions to the gauged nonlinear Schrödinger equation on the plane
cites work: Soliton solutions to the gauged nonlinear Schrödinger equation on the plane
cites work: The Self-Duality Equations on a Riemann Surface
cites work: Representation theory and integration of nonlinear spherically symmetric equations to gauge theories
cites work: Self-dual Chern-Simons vortices
full work available at URL: 0003-4916(91)90208-p
OpenAlex ID: W2002436942
description: scientific article; zbMATH DE number 4210686