Semilocal Self-Dual Chern-Simons Solitons and Toda-type Eqations

TL;DR

This paper explores self-dual soliton solutions in a nonrelativistic Chern-Simons theory with SU(N) and U(1) symmetries, providing exact static and time-dependent solutions, including in external magnetic fields.

Contribution

It introduces new self-dual soliton solutions in a nonrelativistic Chern-Simons model with specific gauge symmetries, including exact static and dynamic solutions.

Findings

Existence of static zero-energy self-dual solitons.

Derivation of exact static soliton solutions.

Time-dependent solutions in external magnetic fields.

Abstract

We consider a nonrelativistic Chern-Simons theory of planar matter fields interacting with the Chern-Simons gauge field in a $SU(N)_{global} \times U(1)_{local}$ invariant fashion. We find that this model admits static zero-energy self-dual soliton solutions. We also present a set of exact soliton solutions. The exact time-dependent solutions are also obtained, when this model is considered in the background of an external uniform magnetic field.