
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 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 spatial dimensions. For , we can analytically solve the non-linear differential equation for an important class of single-field potentials; for , 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.
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