# Compact Q-balls and Q-shells in the CPN type models

## TL;DR

This paper demonstrates the existence of finite energy compact Q-balls and Q-shells in CPN models with an odd number of scalar fields and V-shaped potentials, providing explicit solutions in 3+1 dimensions.

## Contribution

It introduces new compact solutions in CPN models with odd scalar fields, detailing their properties and energy-charge relationship.

## Key findings

- Q-balls for N=1 and N=3
- Q-shells for higher odd N
- Energy scales as E~|Q|^5/6

## Abstract

We show that the CPN model with odd number of scalar fields and V-shaped potential possesses finite energy compact solutions in the form of Q-balls and Q-shells. The solutions were obtained in 3+1 dimensions. Q-balls appears for N=1 and N=3 whereas Q-shells are present for higher odd values of N. We show that energy of these solutions behaves as E~|Q|^5/6, where Q is the Noether charge.