Q -balls in DBI type k field theory

Abstract

We of $Q$-balls in Dirac-Born-Infeld type $k$ field theory, whose action includes a nonlinear kinetic term, $\sqrt{1\ensuremath{-}b{g}^{\ensuremath{\mu}\ensuremath{\nu}}{\ensuremath{\partial}}_{\ensuremath{\mu}}{\ensuremath{\phi}}^{a}{\ensuremath{\partial}}_{\ensuremath{\nu}}{\ensuremath{\phi}}^{a}}/b$. Specifically, for two potentials, ${V}_{3}={m}^{2}{\ensuremath{\phi}}^{2}/2\ensuremath{-}\ensuremath{\mu}{\ensuremath{\phi}}^{3}+\ensuremath{\lambda}{\ensuremath{\phi}}^{4}$ and ${V}_{4}={m}^{2}{\ensuremath{\phi}}^{2}/2\ensuremath{-}\phantom{\rule{0ex}{0ex}}\ensuremath{\lambda}{\ensuremath{\phi}}^{4}+{\ensuremath{\phi}}^{6}/{M}^{2}$, we survey equilibrium solutions for the whole parameter space and analyze their stability through the use of catastrophe theory. Our analysis shows that ${V}_{3}$ and ${V}_{4}$ models fall into fold catastrophe and cusp catastrophe types, respectively, just as for canonical $Q$-balls. We also find that, as long as the absolute minimum of $V(\ensuremath{\phi})$ is located at $\ensuremath{\phi}=0$, equilibrium solutions exist without any additional constraint on charge $Q$ no matter how large $b$ (nonlinearity) is.