Investigations into an Unobserved Photonic Law of Nature (Paper IV): Torsional Boundary States in Warped Compactifications — An Effective APS-Type Index Formula with Nieh-Yan Contributions

This is the first of a new set of three, where we continue to expand upon our initial work. Hercule Poirot had his suspects, we have our hidden variables. Poirot, however, had the distinct advantage of a closed room; our unobserved laws operate in arbitrary dimension without a smoking gun in sight. Following the Topological Emergence Principle, we de- rive an effective APS-type index formula including torsion-dependent contributions for a classical gauge field confined to the boundary of a warped extra dimension. While previ- ous work in this program established the general Riemann-Cartan holographic framework, this manuscript moves to a specific, realistic compactification geometry: a slice of AdS5 (a Randall-Sundrum throat) permeated by a background torsional flux. By evaluating the Nieh-Yan invariant explicitly within this warped background, we derive the corresponding torsion-dependent contribution to the bulk spectral asymmetry within the effective frame- work adopted here. Crucially, we formulate and analyze the generalized equations governing the gauge-field zero mode coupled to this torsional background. Within the effective model, we show that the torsion-dependent contribution can compensate the effective anomaly- inflow contribution, leading to the massless gauge zero-mode localizing on the infrared (IR) boundary brane. This provides an effective geometric mechanism for the Holographic Pho- ton Law: the four-dimensional photon remains structurally intact (dF = 0) because its wavefunction localization is topologically protected by the Nieh-Yan invariant of the bulk geometry.

@article{deceuster2026_76-investigations-in,
  title = {Investigations into an Unobserved Photonic Law of Nature (Paper IV): Torsional Boundary States in Warped Compactifications — An Effective APS-Type Index Formula with Nieh-Yan Contributions},
  author = {De Ceuster, Peter},
  year = {2026},
  month = {02},
  institution = {SIG Labs},
  doi = {10.5281/zenodo.21598615},
  url = {https://peterdeceuster.uk/papers/76-investigations-into-an-unobserved-photonic-law-of-nature},
  note = {Full text available at https://peterdeceuster.uk/articenter/work/four.pdf}
}