d-Dimensional oscillating scalar field lumps and the dimensionality of space

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(ϕ)=∑n=1hgnn!ϕn. Assuming spherical symmetry and if V″<0 for a range of values of ϕ(t,r), such configurations exist if: (i) spatial dimensionality is below an upper-critical dimension dc; (ii) their radii are above a certain value Rmin. Both dc and Rmin are uniquely determined by V(ϕ). For example, symmetric double-well potentials only sustain such configurations if d⩽6 and R2⩾d[3(23/2/3)d−2]−1/2. Asymmetries may modify the value of dc. All main analytical results are confirmed numerically. Such objects may offer novel ways to probe the dimensionality of space.