CFT-approach to Rotating Field Lumps in Attractive Potential

TL;DR

This paper investigates how relativistic effects influence the stability of non-topological solitons in a (2+1)-dimensional setting, highlighting the role of conformal symmetry and its violation.

Contribution

It introduces a CFT-based approach to analyze rotating field lumps, emphasizing the impact of relativistic corrections on their stability and symmetry properties.

Findings

Relativistic corrections break conformal symmetry in the model.

Exponential growth modes indicate instability due to relativistic effects.

Exact expressions for energy and angular momentum are derived under unbroken symmetry.

Abstract

We demonstrate the importance of relativistic corrections for the study of the stability of $(2+1)$-dimensional non-topological solitons with quartic self-interaction in the low-energy limit. This result is explained by the restoration of conformal symmetry in the non-relativistic limit. Particularly, the corresponding cubic Gross-Pitaevskii equation supports scale-free non-topological solitons. An unbroken conformal symmetry provides the additional degeneration that allows for the exact result for the energy and angular momentum of the stationary classical solutions. We study the violation of conformal symmetry by relativistic corrections. The emergence of exponentially growing modes on the classical background is demonstrated using analytical approximations and numerical calculations.