Towards spinning $U(1)$ gauged non-topological solitons in the model with Chern-Simons term

TL;DR

This paper constructs and analyzes finite-energy, spinning non-topological solitons in a (2+1)-dimensional Maxwell-Chern-Simons model with a complex scalar, revealing their stability, charge bounds, and symmetry properties.

Contribution

It introduces new non-topological soliton solutions with angular momentum in a Maxwell-Chern-Simons framework, including their numerical stability and symmetry features.

Findings

Solutions possess finite energy, charge, and angular momentum.

They are numerically demonstrated to be kinematically stable.

The solutions exhibit a lower bound on charge and potential conformal symmetry restoration.

Abstract

We obtain localized field configurations with finite energy in a ($2+1$)-dimensional model with Maxwell and Chern-Simons gauge terms coupled to a massive complex scalar field. These non-topological solitons are characterized by the $U(1)$ frequency and a winding number. Thus, the solutions possess Noether charge and non-trivial angular momentum, which is not quantized in contrast to the topological case. We study the solitons and their integral characteristics numerically and demonstrate that they are kinematically stable. The obtained solutions allow for the thin-wall approximation in some region of frequencies. For each winding number, the Noether charge has a lower bound that coincides with an isolated point, where the non-relativistic conformal symmetry seems to be restored.