Q-balls across dimensions

TL;DR

This paper generalizes the concept of Q-balls, non-topological solitons, to arbitrary spatial dimensions, providing analytical solutions and approximations for different regimes, with applications to vacuum decay.

Contribution

It extends the analysis of Q-balls to $d$ dimensions, offering analytical solutions in 1D and approximations in higher dimensions, including sub-leading corrections.

Findings

Analytical solutions for Q-balls in 1D

Approximate solutions in higher dimensions for large Q-balls

Applications to vacuum-decay bounce solutions

Abstract

Scalars carrying a conserved global charge $Q$ can form stable localized field configurations composed of a large number of particles. These non-topological solitons are spherically symmetric and are called Q-balls. While usually analyzed in three spatial dimensions, these solitons can be straightforwardly generalized to $d$ spatial dimensions. For $d=1$, we can analytically solve the non-linear differential equation for an important class of single-field potentials; for $d>1$, we can analytically approximate the solutions in the thin-wall or large Q-ball regime, including the first sub-leading correction consistently. Since the underlying differential equations have the same form as vacuum-decay bounce solutions, our results find applications there, too.