Emergent Vacuum Lensing from Holonomy–Radion Dynamics and θ-Interfaces in Compactified QED

This work presents an effective description of compactified QED in which the vacuum state is characterized by two joint low-energy variables: the Wilson-line holonomy (a) around the compact circle and the radion (ϕ), understood as the dilatonic mode controlling its size. Its central claim is that vacuum lensing should be understood not merely as geometric light bending, but more broadly as a set of linked observational channels generated by one and the same vacuum state (a,ϕ). In the CP-even sector, this state induces an Euler–Heisenberg-type response, leading to birefringence, phase delay, and refractive propagation effects in external electromagnetic backgrounds. In the CP-odd sector, the vacuum exhibits an axion-type magnetoelectric response whose physical content becomes observable through gradients of θ in the bulk and through physical Δθ jumps across interfaces; in the thin-wall limit, such interfaces behave as effective lossless Hall sheets and mix photon polarizations. When radion dynamics and four-dimensional gravity are included, vacuum energy and wall tension additionally source a conservative weak-field Einstein-frame metric backreaction, providing a gravitational channel complementary to the optical and interfacial ones. The key achievement of the manuscript is therefore not an isolated signature, but a unified scheme that connects local response data derived from the compactified fermionic sector to physical vacua, walls, and bubbles, and from there to observable channels: birefringent transport in the bulk, polarization mixing at θ-interfaces, and weak-field metric lensing. In this sense, the manuscript organizes these effects as mutually consistent readouts of a single holonomy–radion vacuum state and demonstrates their coexistence in a controlled multi-vacuum bubble benchmark.