A note on Chern–Simons solitons—A type III vortex from the wall vortex

Abstract

We study some properties of topological Chern–Simons vortices in 2 + 1 dimensions. As has already been understood in the past, in the large magnetic flux limit, they are well described by a Chern–Simons domain wall, which has been compactified on a circle with the symmetric phase inside and the asymmetric phase on the outside. Our goal is two-fold. First we want to explore how the tension depends on the magnetic flux discretized by the integer n. The BPS case is already known, but not much has been explored about the non-BPS potentials. A generic renormalizable potential has two dimensionless parameters that can be varied. Variation of only one of them leads to a type I and type II vortex, very similar to the Abrikosov–Nielsen–Olesen (ANO) case. Variation of both the parameters leads to a much richer structure. In particular we have found a new type of vortex, which is type I-like for small flux and then turns type II-like for larger flux. We could tentatively denote it a type III vortex. This results in a stable vortex with number of fluxes which can be greater than one. Our second objective is to study the Maxwell–Chern–Simons theory and understand how the large n limit of the CS vortex is smoothly connected with the large n limit of the ANO vortex.