Vacuum as a Medium: Holonomy-Driven Birefringence and Axion θ-Interfaces in Compactified QED

Can empty space behave like an optical material?This work explores that question in compactified quantum electrodynamics, where quantum effects associated with charged particles make the vacuum behave not as a completely inert void, but as an extremely weak optical medium with a subtle and internally organized structure of response. Earlier studies of compactified QED had already shown that compact dimensions can modify photon propagation and induce anisotropic vacuum response, while related work on R3,1×S1 backgrounds with magnetic flux identified parity-breaking terms. More recent axion literature has clarified the general monodromic form of axion-photon couplings, including those descending from extra dimensions. The novelty of the present work lies elsewhere: it develops an optics-first realization of compactified QED in which both bulk Euler–Heisenberg birefringence and CP-odd theta-interface response are governed by the same holonomy-dependent kernel, and it carries that structure all the way to explicit observables. In the presence of an external magnetic field, the symmetric part of the response produces vacuum birefringence during bulk propagation, while its chiral difference is encoded by an axion term and becomes observable when theta varies in space or jumps across an interface, producing polarization rotation and mode mixing. The work derives constitutive relations, interface reflection and transmission matrices, a complete Jones-to-Stokes polarization pipeline, and a controlled regime of validity with matching near Kaluza–Klein crossings. Situated at the intersection of quantum electrodynamics, effective field theory, nonlinear vacuum optics, and axion/topological electrodynamics, it is best understood not as the first appearance of a monodromic axion-photon coupling, but as a unified analytic framework that turns holonomy-dependent quantum-field-theory structure into concrete magneto-optical predictions. In a broader perspective, this picture naturally points toward coupling holonomy to the compactification radius, or radion, leading to a richer holonomy–radion effective field theory and opening the way to describing the vacuum as a medium whose response is jointly shaped by the Wilson-line phase and the size of the compact dimension.