CFT approach to rotating field lumps in an attractive potential

We demonstrate the importance of relativistic corrections for the study of the stability of (2+1)-dimensional nontopological solitons with quartic self-interaction in the low-energy limit. This result is explained by the restoration of conformal symmetry in the nonrelativistic limit. Particularly, the corresponding cubic Gross-Pitaevskii equation supports scale-free nontopological 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.