Effective Field Theory of a Fractal Vacuum: A Unified Topological Framework

We present a nonlocal scalar-tensor framework, the Fractal Dielectric Network (FDN), to address the emergence of gravitational effects from a discrete vacuum infrastructure. By promoting the scalar order parameter —representing local vacuum coherence—to a nonlocal regime via a fractional kinetic operator , we identify a distinctive boundary-layer effect at screening interfaces. We demonstrate that this mechanism induces an anisotropic modification of the effective optical metric, leading to a quadrupolar modulation of the photon ring geometry in strong-gravity environments. This signature is asymptotically motivated by the fractal connectivity of the network and remains potentially distinguishable from Kerr spin asymmetries and frequency-dependent plasma effects, providing a testable handle for next-generation interferometry (ngEHT).I.