Compact Q-balls and Q-shells in a multi-component $\mathbb{C}P^N$ model

TL;DR

This paper investigates multi-component $ ext{CP}^N$ models with V-shaped potentials, revealing solutions combining compact Q-balls and Q-shells, and analyzing their stability and energy-charge relations.

Contribution

It introduces novel compact Q-ball and Q-shell solutions in multi-component $ ext{CP}^N$ models with V-shaped potentials, including harbor-type configurations.

Findings

Solutions are combinations of compact Q-balls and Q-shells.

Energy scales as $E o |Q|^eta$ with $eta<1$, similar to standard Q-balls.

Solutions are suggested to be classically stable based on energy-charge ratios.

Abstract

Coupled multi-component $\mathbb{C}P^N$ models with V-shaped potentials are analyzed. It is shown that the model has solutions being combinations of compact Q-balls and Q-shells. The compact nature of solutions permits the existence of novel harbor-type solutions having the form of Q-balls sheltered by Q-shells. The relation between the energy $E$ and Noether charge $Q$ is discussed both analytically and numerically. The energy of the solutions behaves as $E\sim |Q|^\alpha,~\alpha<1$, i.e., as for the standard Q-ball. Furthermore, the ratio $E/Q$ for various configurations in the multi-component model suggests that the solutions are at least classically stable.