Abstract
p-Balls are topological defects in (D, 1) dimensions constructed with $$ \mathrm{\mathcal{M}}\ge 1 $$ scalar fields which depend radially on only 2 ≤ p ≤ D − 2 spatial dimensions. Such defects are characterized by an action that breaks translational invariance and are inspired on the physics of a brane with D − p extra dimensions. Here we consider the issue of localization of bosonic states described by a scalar field Φ sufficiently weak to not disturb sensibly the defect configuration. After describing the general formalism, we consider some specify examples with $$ \mathrm{\mathcal{M}} $$ = 1, 2 and 3, looking for some region of parameters where bound and resonant bosonic states can be found. We investigate the way the influence of the defect structure, number of radial dimensions and coupling between the fields are related to the occurrence of bound and resonant states.
Highlights
In general codimension-1 brane models can be treated using the first-order formalism [29]
Abstract: p-Balls are topological defects in (D, 1) dimensions constructed with M ≥ 1 scalar fields which depend radially on only 2 ≤ p ≤ D − 2 spatial dimensions
In this work we introduced p-balls as topological defects in (D, 1) dimensions constructed with M ≥ 1 scalar fields which depend radially on only 2 ≤ p ≤ D − 2 spatial dimensions
Summary
In order to describe the system via first-order differential equations, we implement the BPS formalism such that the total energy can be written as. Whenever these first-order equations are satisfied and using (2.3), the total energy reads. At this point we observe the integrand can be transformed in a total derivative whether N = 2p − 2. We make the scaling transformation r → λr and φ(r) → φ(λr), corresponding to a change in the energy given by E → Eλ, and impose (∂Eλ)/(∂λ)|λ=1 = 0. This leads to the following restrictions on N and p: i) for p = 1, N = 0; ii) for p = 2,. The energy EBPS given by eq (2.13) is fixed and it becomes a true topological BPS bound
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