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

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.