Compact Q-balls and Q-shells within a $CP^N$ Skyrme-Faddeev type model

TL;DR

This paper investigates the existence, stability, and properties of compact Q-balls and Q-shells in an extended $CP^N$ Skyrme-Faddeev model with quartic derivatives, revealing how higher-order terms influence these non-topological solitons.

Contribution

It introduces a detailed analysis of compact Q-balls and Q-shells within a complex Skyrme-Faddeev-type model incorporating quartic derivative terms, expanding understanding beyond analytic potential models.

Findings

Quartic derivative terms stabilize compact solutions.

The energy-charge relationship is significantly affected by higher-order terms.

Conditions for existence and stability of solutions are established.

Abstract

While $CP^N$ models with analytic potentials are known to support finite-energy compact Q-ball and Q-shell solutions, their behavior in more complex Lagrangian frameworks remains a subject of active research. This work explores these non-topological structures within an extended Skyrme-Faddeev-type model that incorporates quartic derivative terms. In this context, harmonic time dependence and the presence of quartic terms constitute two independent stabilization mechanisms that allow the configurations to circumvent Derrick's scaling argument. We investigate the necessary conditions for the existence of these solutions and analyze the influence of quartic terms on the properties of the resulting compactons, specifically examining the $E(Q)$ relationship between energy and Noether charge. Our findings provide valuable insights into the stability and characteristics of compact boson stars within $CP^N$ models featuring higher-order derivative terms.