Generalized Models for Spinning Field Lumps on Plane

TL;DR

This paper introduces generalized models for spinning field lumps on a plane, demonstrating their stability, symmetry restoration at low energies, and the influence of nonlinear terms on the non-relativistic regime.

Contribution

It develops a new class of models with bounded nonlinear potentials that ensure stability and symmetry restoration, extending previous models with negative quartic interactions.

Findings

Solutions exhibit kinematical stability.

Full Schrödinger symmetry is restored at low energies.

Nonlinear terms determine non-relativistic regime behavior.

Abstract

We study planar non-topological solitons in models with nonlinear potentials that are bounded from below. These models provide consistent completion for the classical consideration at any energy scale. The properties of our solutions indicate the kinematical stability, which is unachievable in the previously studied model with negative quartic self-interaction. Remarkably, our generalization preserves restoration of the full Schr\"{o}dinger symmetry at low energies, including scale invariance (dilatation) and special conformal symmetry. Our numerical calculations and analytical approximations demonstrate that the details of non-relativistic regime are defined by the lowest nonlinear $U(1)$-invariant term.