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 with Dirac--Born--Infeld (DBI) worldvolume dynamics. 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 to the semiclassically admissible flux window and endow the membrane with a worldvolume $U(1)$ gauge field carrying quantized monopole flux $n\in\mathbb{Z}$. Evaluating the full DBI energy, we find that the energetically preferred branch collapses toward a microscopic core rather than stabilizing at finite radius. For nonzero monopole flux, however, the energy remains finite in the collapsed limit, yielding a stable flux-supported particle-like remnant whose mass is set by the wall scale and conserved flux. We call these objects topolons. Within the admissible sector, the energy analysis separates stable collapsed remnants from runaway vacuum-decay configurations, identifying the sector relevant for cosmological relic formation. At macroscopic distances, topolons behave as heavy localized states and constitute a concrete dark-relic candidate. More broadly, the construction provides the nonperturbative remnant sector of an economical three-form framework in which homogeneous four-form flux may neutralize the dominant permanent vacuum-energy contribution, while a dynamical scalar supplies the temporary positive energy required for no-boundary inflation. The detailed cosmological abundance, residual late-time vacuum energy, and phenomenology are left for future work.