Q-balls across dimensions

Scalars carrying a conserved global charge Q can form stable localized field configurations composed of a large number of particles. These nontopological 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 nonlinear 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 subleading correction consistently. Since the underlying differential equations have the same form as vacuum-decay bounce solutions, our results find applications there, too.