Energy Landscape of d-Dimensional Q-balls

Abstract

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 $V(\varphi {\varphi }^{†})={\sum }_{n=1}^3{a}_n(\varphi {\varphi }^{†}{)}^n$, 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 $Q_{\min }\sim \exp (d)$. We also briefly investigate the existence of $Q$-clouds in $d$ dimensions.

13 pages, 10 figures, final version to appear in Physical Review D. Small corrections

References in corpus (1)

• d-dimensional Oscillating Scalar Field Lumps and the Dimensionality of Space

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