Topolons: Stable Particle-Like Remnants of Collapsed Vacuum Bubbles in a Three-Form Gauge Sector

Abstract

We study a three-form gauge sector in four spacetime dimensions coupled to electrically charged spherical membranes whose worldvolume dynamics are governed by a Dirac–Born–Infeld action. The associated four-form field strength has no local propagating degrees of freedom and contributes a branch-dependent vacuum energy. Motivated by the Hartle–Hawking–Wu selection argument, we restrict attention to the semiclassically admissible four-form flux window for which the Hartle-Hawking wave function has support. We then endow the bubble wall with a worldvolume U(1) gauge field carrying quantized monopole flux \(n \in \mathbb {Z}\) and evaluate the full DBI energy of the resulting spherical configurations. We show that the energetically preferred branch collapses toward a microscopic core rather than stabilizing at finite radius, but for nonzero monopole flux the energy does not vanish in the collapsed limit. Instead, the bubble relaxes to a finite-energy remnant whose mass is set by the wall scale and the conserved flux. We interpret these objects as stable flux-supported particle-like states, which we call topolons. Within the admissible sector, the effective energy analysis distinguishes stable collapsed remnants from the contrasting runaway vacuum-decay channel, thereby isolating the sector relevant for cosmological relic formation. At macroscopic distances, topolons behave as heavy localized states and provide a concrete microphysical realization of a dark relic candidate. The detailed cosmological abundance and phenomenology are left for future work. More broadly, the present construction supplies the nonperturbative remnant component of an economical three-form framework in which the homogeneous four-form flux may neutralize the dominant permanent vacuum-energy contribution, while a dynamical scalar supplies the temporary positive energy required for a no-boundary inflationary history. Additional four-form dynamics, another sector, or presently unknown physics may leave the small residual vacuum energy observed at late times. The present paper does not claim a complete unified cosmology, but establishes the microscopic topolon sector required for such a program.