# Review of non-topological solitons in theories with $U(1)$-symmetry

## TL;DR

This review comprehensively discusses non-topological solitons with $U(1)$-symmetry, including Q-balls, condensates, and boson stars, highlighting their properties, stability, and extensions in various theoretical models.

## Contribution

It provides a detailed synthesis of the properties, stability, and extensions of non-topological solitons in theories with $U(1)$-symmetry, including recent developments.

## Key findings

- Analysis of stability conditions for Q-balls and related solitons
- Connection between solitons with additional degrees of freedom and basic Q-balls
- Discussion of gauged Q-balls and boson stars in gravitational theories

## Abstract

We provide a review of non-topological solitonic solutions arising in theories with a complex scalar field and global or gauge $U(1)$-symmetry. It covers Q-balls, homogeneous charged scalar condensates, and nonlinear localized holes and bulges in a classically stable condensate. A historical overview is followed by the discussion of properties of solutions, including their stability, from different perspectives. Solitons in models with additional massive degrees of freedom are also revisited, and their relation to one-field Q-balls is showed. We also discuss theories with a gauge field giving rise to gauged Q-balls and theories with dynamical gravity giving rise to boson stars.