Investigating an Unobserved Photonic Law (Paper III of III): Torsional Anomaly Inflow — Riemann-Cartan Holography and the Protected Photon

We extend the Holographic Photon Continuity framework into Riemann-Cartan geometry (U4) to analyze the dynamical interaction between extra-dimensional topological currents and gravitational torsion. Standard general relativity assumes a torsion-free Levi-Civita connection; however, coupling the bulk Higgs-photon sheaf to a non-symmetric affine con- nection fundamentally alters the spectral geometry of the system. We demonstrate that mapping the holographic boundary coupling to a Riemann-Cartan background naturally leads to an APS-type index formulation including torsion-dependent corrections, allowing the Nieh-Yan invariant together with torsion-dependent characteristic classes to contribute to the bulk obstruction class. Consequently, the Holographic Photon Law (Lholo), which protects the integrity of the 4D Bianchi identity (dF = 0), becomes strictly torsion-dependent. This implies that macro- scopic gravitational torsion acts as a direct catalyst for anomaly inflow, dynamically shifting the quantized index charge (Qindex) flowing from the extra dimensions. This formulation predicts profound cosmological and astrophysical signatures: photons traversing torsion- rich environments—such as primordial defect backgrounds or the vicinities of ultra-dense fermionic spin matter—must exhibit anomalous phase shifts and topological vacuum birefrin- gence. Ultimately, this framework establishes a mathematically consistent, testable bridge between Einstein-Cartan gravity, derived category topology, and observable quantum op- tics, providing a microscopic derivation, proving interpretation uniqueness, and identifying testable observables.

@article{deceuster2026_82-investigating-an-,
  title = {Investigating an Unobserved Photonic Law (Paper III of III): Torsional Anomaly Inflow — Riemann-Cartan Holography and the Protected Photon},
  author = {De Ceuster, Peter},
  year = {2026},
  month = {02},
  institution = {SIG Labs},
  doi = {10.5281/zenodo.21557769},
  url = {https://peterdeceuster.uk/papers/82-investigating-an-unobserved-photonic-law-paper-iii-of},
  note = {Full text available at https://peterdeceuster.uk/articenter/work/light3.pdf}
}