Q-balls across dimensions

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.

Figures (7)

• Figure 1: Effective potential $V(f)$ from Eq. \ref{['eq:potential']} for $\kappa =1/2$.
• Figure 2: $E/(m_\phi Q)$ for $d=1$ as a function of $\kappa$ for $\omega_0/m_\phi = 0.01$ (left) and $0.3$ (right). Different colors correspond to different $n$, and stable Q-balls are in the region $E/(m_\phi Q) < 1$, i.e. below the black dashed line.
• Figure 3: $E/(m_\phi Q)$ for $d=n=1$ as a function of $Q$ for $\omega_0/m_\phi = 0.01$. Different colors correspond to different $\kappa$ regions and the arrow indicate flow of decreasing $\kappa$.
• Figure 4: Q-ball profiles $f(\rho)$ for fixed $n=3$ and several $d$ (left) and fixed $d=4$ and several $n$ (right). The solid lines are the numerical solutions, the dashed lines our analytical approximations from Eq. \ref{['eq:f_new']} with radius from Eq. \ref{['eq:radius']}. Notice that we picked rather large $\kappa$ in order to see at least some deviations.
• Figure 5: Q-ball radii for fixed $n=2$ and several $d$ (left) and fixed $d=4$ and several $n$ (right). The solid lines are the numerical solutions, the dashed lines our analytical approximations from Eq. \ref{['eq:radius']}.