Excited solutions in a Skyrme--Chern-Simons model in $2+1$ dimensions

TL;DR

This paper investigates excited solutions in a 2+1 dimensional Skyrme--Chern-Simons model, highlighting the need for a Lagrange multiplier method and analyzing their properties and energy behaviors.

Contribution

It introduces a Lagrange multiplier approach to find excited solutions and examines their characteristics and energy patterns in the model.

Findings

Excited solutions are characterized by an integer p, with p≠0.

The global charges depend non-traditionally on parameters.

The presence of the Chern-Simons term does not change the energy hierarchy.

Abstract

We study excited solutions in a Skyrme--Chern-Simons theory in $2+1$ dimensions. In particular, we emphasize the necessity of using a Lagrange multiplier method to obtain excited solutions, due to the appearance of a discontinuity when using a constraint compliant parametrization. These solutions are characterized by an integer number $p$, excited solutions corresponding to $p\neq 0$. The dependence of the global charges on the parameters is analyzed, showing non-standard behaviors. We also find that the presence of the Skyrme--Chern-Simons term does not alter significantly the pattern of energy levels, so $p=0$ solutions (fundamental solutions) have always the minimal energy.