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

TL;DR

This paper demonstrates the existence of long-lived, oscillating scalar field lumps in various spatial dimensions, revealing how their stability depends on the potential and dimensionality, and suggesting they could be used to probe the number of spatial dimensions.

Contribution

The study provides analytical and numerical evidence for scalar field lumps' existence in different dimensions, establishing critical conditions related to potential shape and size, and linking these objects to the dimensionality of space.

Findings

Lumps exist below a critical dimension $d_c$ for given potentials.

Stability depends on the size of the lumps and the potential parameters.

Numerical results confirm analytical predictions.

Abstract

Extremely long-lived, time-dependent, spatially-bound scalar field configurations are shown to exist in $d$ spatial dimensions for a wide class of polynomial interactions parameterized as $V(\phi) = \sum_{n=1}^h\frac{g_n}{n!}\phi^n$. Assuming spherical symmetry and if $V''<0$ for a range of values of $\phi(t,r)$, such configurations exist if: i) spatial dimensionality is below an upper-critical dimension $d_c$; ii) their radii are above a certain value $R_{\rm min}$. Both $d_c$ and $R_{\rm min}$ are uniquely determined by $V(\phi)$. For example, symmetric double-well potentials only sustain such configurations if $d\leq 6$ and $R^2\geq d[3(2^{3/2}/3)^d-2]^{-1/2}$. Asymmetries may modify the value of $d_c$. All main analytical results are confirmed numerically. Such objects may offer novel ways to probe the dimensionality of space.