We investigate the properties of $Q$-balls in $d$ spatial dimensions. First, a generalized virial relation for these objects is obtained. We then focus on potentials $V(\phi\phi^{ \dagger})= \sum_{ n=1}^{ 3} a_n(\phi\phi^{ \dagger})^n$, where $a_n$ is a constant and $n$ is an integer, obtaining variational estimates for their energies for arbitrary charge $Q$. These analytical estimates are contrasted with numerical results and their accuracy evaluated. Based on the results, we offer a simple criterion to classify ``large'' and ``small'' $d$-dimensional $Q$-balls for this class of potentials. A minimum charge is then computed and its dependence on spatial dimensionality is shown to scale as $Q_{ \rm min} \sim \exp(d)$. We also briefly investigate the existence of $Q$-clouds in $d$ dimensions.
Categories: hep-th