Topological structure of the many vortices solution in Jackiw-Pi model

TL;DR

This paper constructs multi-vortex solutions in the Jackiw-Pi model, analyzing their topological structure via gauge potential decomposition and relating vortex solutions to topological invariants like Hopf indices and Brouwer degrees.

Contribution

It introduces a method to explicitly construct multi-vortex solutions in the Jackiw-Pi model and explores their topological properties using the ta-mapping approach.

Findings

Multi-vortex solutions depend on 5M parameters.

Topological charge relates to Hopf indices and Brouwer degrees.

Flux quantization is established for these solutions.

Abstract

We construct an M-solitons solutions in Jackiw-Pi model depends on 5M parameters(two positions, one scale, one phase per solition and one charge of each solution). By using \phi -mapping method, we discuss the topological structure of the self-duality solution in Jackiw-Pi model in terms of gauge potential decomposition. We set up relationship between Chern-Simons vortices solution and topological number which is determined by Hopf indices and and Brouwer degrees. We also give the quantization of flux in this case.