From Q-walls to Q-balls

TL;DR

This paper investigates Q-ball solitons in various dimensions with flat potentials, deriving energy-charge relations, analyzing stability of wall and string configurations, and discussing their potential cosmological significance.

Contribution

It provides a general energy-charge relation for Q-balls in arbitrary dimensions and links stability analysis of Q-wall configurations to supersymmetric quantum mechanics.

Findings

Energy scales as Q^{d/(d+1)} in d dimensions.

Q-wall and Q-string configurations are unstable.

These configurations can have long lifetimes, relevant to cosmology.

Abstract

We study $Q$-ball type solitons in arbitrary spatial dimensions in the setting recently described by Kusenko, where the scalar field potential has a flat direction which rises much slower than $\phi^2$. We find that the general formula for energy as a function of the charge is, $E_d\sim Q_d^{(d/d+1)}$ in spatial dimension $d$. We show that the Hamiltonian governing the stability analysis of certain $Q$-wall configurations, which are one dimensional $Q$-ball solutions extended to planar, wall-like configurations in three dimensions, can be related to supersymmetric quantum mechanics. $Q$-wall and $Q$-string (the corresponding extensions of 2 dimensional $Q$-balls in 3 spatial dimensions) configurations are seen to be unstable, and will tend to bead and form planar or linear arrays of 3 dimensional $Q$-balls. The lifetime of these wall-like and string-like configurations is, however, arbitrarily large and hence they could be of relevance to cosmological density fluctuations and structure formation in the early Universe.