Radion-Supported Gravitating Solitons in Flux-Stabilized Kaluza–Klein Compactifications

We provide a classical effective-field-theory formulation for localized finite-energy con
figurations possessing an effective gravitational mass scale via warped compactification
of an Einstein–Yang–Mills–Higgs system. Working within the lowest-mode Kaluza–Klein
truncation—valid provided gradients and defect energies remain below the first KK exci
tation scale—we define a localized radion core as a region in which the radion, gauge, and
Higgs profiles depart from their asymptotic compactification values, creating a finite-energy
soliton configuration. Tracking the logarithmic radion field σ = lnΨ through a Weyl confor
mal transformation, we derive its Einstein-frame kinetic term and identify the canonically
normalized field. By explicitly integrating a topologically normalized harmonic flux over
the reference metric, we remove scaling ambiguities and derive the Einstein-frame effective
potential within the lowest-mode truncation. After detailing the radion-gauge derivative
mixing and the resulting Effective Field Theory (EFT) expansion, we formulate the fully
coupled nonlinear boundary-value problem for a gravitating monopole sector. The explicit
existence of these radion-supported solitons remains to be established via numerical investi
gation of the resulting system of five coupled nonlinear radial equations for the gauge, Higgs,
radion, and metric functions.