Gauged compact $Q$-balls and $Q$-shells in a multi-component $CP^N$ model

Abstract

We study a multicomponent $CP^N$ model's scalar electrodynamics. The model contains $Q$-balls and $Q$-shells, which are nontopological compact solitons with time dependency $e^{iωt}$. Two coupled $CP^N$ models can decouple locally if one of their $CP^N$ fields takes the vacuum value. Because of the compacton nature of solutions, $Q$-shells can shelter another compact $Q$-ball or $Q$-shell within their hollow region. Even if compactons do not overlap, they can interact through the electromagnetic field. We investigate how the size of multicompacton formations is affected by electric charge, with a focus on structures with nonzero or zero total net charge.

Figures (9)

• Figure 1: The $CP^3$--$CP^{23}$$Q$-ball -- $Q$-shell configuration with zero net electric charge $\bar{Q}_1+\bar{Q}_2=0$. (a) Radial profile functions $f(r)$, $g(r)$ (gauged case -- solid lines; nongauged case -- dashed lines), electric field $E(r)$ and electric charge density $\rho (r)$ (dotted line). (b) Energy density for gauged (solid line) and nongauged (dashed line) cases. We employ $(\alpha,\beta,\lambda)=(1.0, 1.0, 1.0)$ for the numerical analysis in this paper, but qualitatively, it is not necessary to fix the specific values.
• Figure 2: (a) Profile function $f(r)$ for the gauged model (solid line) parametrized by $\omega_1=3.0$ and $q^{(1)}=1.0$ and the non-gauged profile function $f_{NG}(r)$ (dashed line) for $\widetilde{\omega}_1=\omega_1-eq^{(1)}\alpha_0=2.5$ where $\alpha_0=0.5$. (b) Profile function $g(r)$ for the gauged model (solid line) parametrized by $\omega_1=3.0$ and $q^{(2)}=-0.071$ and the nongauged profile function $g_{NG}(r)$ (dashed line) for $\widetilde{\omega}_2=\omega_2-eq^{(2)}A_t(R_2^{\rm(out)})\approx 3.029$ where $A_t(R_2^{\rm(out)})=0.418$.
• Figure 3: The $CP^3$--$CP^{23}$$Q$-ball -- $Q$-shell configuration with negative net electric charge $\bar{Q}_1+\bar{Q}_2<0$. (a) Radial profile functions $f(r)$, $g(r)$ (gauged case -- solid lines; nongauged case -- dashed lines), the electric field $E(r)$, and the electric charge density (dotted line). (b) Energy density for gauged (solid line) and nongauged (dashed line) cases.
• Figure 4: The $CP^3$--$CP^{23}$$Q$-ball -- $Q$-shell configuration with positive net electric charge $\bar{Q}_1+\bar{Q}_2>0$. (a) Radial profile functions $f(r)$, $g(r)$ (gauged case -- solid lines; nongauged case -- dashed lines), the electric field $E(r)$, and the electric charge density (dotted line). (b) Energy density for gauged (solid line) and nongauged (dashed line) cases.
• Figure 5: (a) Zero net charge for $\alpha_0=1.0$ and $q^{(1)}=1.0$. (b) Positive net charge for $\alpha_0=1.2$.