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Properties of Non-topological Solitons in Two-dimensional Model With Resurrected Conformal Symmetry

Yulia Galushkina, Eduard Kim, Emin Nugaev, Yakov Shnir

TL;DR

This work investigates non-topological solitons in a two-dimensional conformal field theory and the impact of conformal symmetry on their stability. It first builds a non-relativistic quintic nonlinear Schrödinger model that preserves dilatation and conformal invariance, yielding a bright soliton whose energy and charge are independent of the soliton width due to scale symmetry; linear perturbations reveal only symmetry-related zero modes, implying the absence of nontrivial vibrational or decay modes. A relativistic generalization is then constructed, showing that decay modes reappear with finite rates that vanish in the strict conformal limit ($ω\to m$), thereby linking symmetry restoration to the emergence of dynamical instabilities. The results illuminate how conformal symmetry constrains the excitation spectrum of planar solitons and indicate how relativistic effects qualitatively alter stability, with potential implications for ultralight dark matter and Bose-star contexts.

Abstract

We study properties of non-topological solitons in two-dimensional conformal field theory. The spectrum of linear perturbations on these solutions is found to be trivial, containing only symmetry-related zero modes. The interpretation of this feature is given by considering the relativistic generalization of our theory in which the conformal symmetry is violated. It is explicitly seen that the restoration of this symmetry leads to the absence of decay/vibrational modes.

Properties of Non-topological Solitons in Two-dimensional Model With Resurrected Conformal Symmetry

TL;DR

This work investigates non-topological solitons in a two-dimensional conformal field theory and the impact of conformal symmetry on their stability. It first builds a non-relativistic quintic nonlinear Schrödinger model that preserves dilatation and conformal invariance, yielding a bright soliton whose energy and charge are independent of the soliton width due to scale symmetry; linear perturbations reveal only symmetry-related zero modes, implying the absence of nontrivial vibrational or decay modes. A relativistic generalization is then constructed, showing that decay modes reappear with finite rates that vanish in the strict conformal limit (), thereby linking symmetry restoration to the emergence of dynamical instabilities. The results illuminate how conformal symmetry constrains the excitation spectrum of planar solitons and indicate how relativistic effects qualitatively alter stability, with potential implications for ultralight dark matter and Bose-star contexts.

Abstract

We study properties of non-topological solitons in two-dimensional conformal field theory. The spectrum of linear perturbations on these solutions is found to be trivial, containing only symmetry-related zero modes. The interpretation of this feature is given by considering the relativistic generalization of our theory in which the conformal symmetry is violated. It is explicitly seen that the restoration of this symmetry leads to the absence of decay/vibrational modes.

Paper Structure

This paper contains 5 sections, 26 equations, 3 figures, 1 table.

Table of Contents

  1. Introduction
  2. The model and symmetries
  3. Soliton and excitations
  4. Relativistic generalization
  5. Outlook

Figures (3)

  • Figure 1: Dimensionless integral characteristics $\tilde{E}=\frac{E}{m}, \tilde{Q}=Q$ of relativistic model (\ref{['Rel. model']}) calculated at parameter $\frac{\lambda}{m^{2}}=1$. Dashed line represents plane waves solutions of mass $mQ$ and the cross mark corresponds to conformal theory (\ref{['NR lagrangian']}).
  • Figure 2: Spectrum of decay modes that are described by Eqs.(\ref{['Lin. eqs decay modes']}). In the limit $\omega\to m$ parameter $\gamma_{dec.}$ tends to zero as $C\cdot(m-\omega)^{1.506}$.
  • Figure 3: Decay mode profile at $\omega/m=0.99$ and $\gamma_{dec.}/m=3.74\cdot 10^{-3}$. Scaled soliton profile and ${(-\gamma_{dec.})\frac{\partial g_{\omega}(x)}{\partial \omega}}$ are added for comparison.