Generalized Models for Spinning Field Lumps on Plane

TL;DR

Planar non-topological solitons in $2+1$-D scalar theories with attractive quartic self-interaction are unstable due to potentials unbounded from below. The authors study UV-completed, bounded potentials that preserve Schrödinger symmetry in the non-relativistic limit, examining a conformal quartic model, a sextic-extension, and the Friedberg–Lee–Sirlin (FLS) two-field model. They identify parameter regions where stable Q-tubes exist, show that the non-relativistic limit restores the Schrödinger symmetry (e.g., $H=0$ and $Q$-independence) and that $E(Q)$ curves approach a conformal point, with cusp structures depending on the UV completion. These findings provide symmetry-preserving stabilization mechanisms for planar solitons and yield insights relevant to condensed-matter vortices and dark-matter phenomenology, while clarifying how UV completions can stabilize solitons without breaking NR conformal invariance.

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 Schrödinger 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.

Figures (9)

• Figure 1: Integral characteristics of Q-tubes with different values of the parameter n.
• Figure 2: a) The mechanical potential $U(\tilde{f})$ for different values of $g$; $n = 0$, $\mathrm{w} = 0$. b) Profiles of solitons for different values of $\sigma m^2 / \lambda^2$; $n = 0$, $\mathrm{w} = 0$.
• Figure 3: Integral characteristics of Q-tubes with different values of the parameter $\sigma m^2 / \lambda^2$: a) $n = 0$, b) $n = 1$.
• Figure 4: The value $1 - \omega_{cusp} / m$ for Q-tubes with different values of the parameter $\sigma m^2 / \lambda^2$; n = 0.
• Figure 5: The potential of FLS theory for $\varkappa/h = 1$.