Compact Q-balls and Q-shells within a CPN Skyrme-Faddeev type model

A bstract 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 resulting compactons. Specifically, we examine the scaling relationship between energy and Noether charge, expressed as E ( Q ) ~ | Q | n . Our numerical analysis demonstrates that n < 1, which supports the stability of these solutions against spontaneous fission.