Investigations into an Unobserved Photonic Law of Nature (Paper VI): Holographic Protection of Non-Abelian Sectors — Hypocoercivity, Instanton Gases, and the QCD Mass Gap

We extend the Topological Emergence Principle from U(1) electromagnetism to non-Abelian SU(N) Yang-Mills theories, investigating the geometric origins of the QCD mass gap and topological susceptibility. While standard quantum chromodynamics relies on non-perturbative instanton liquid models to explain the η′ mass via the Witten-Veneziano formula, a rigor- ous geometric derivation remains an open problem. We hypothesize that the non-Abelian vacuum is a topologically protected boundary state of a higher-dimensional bulk. By map- ping the Yang-Mills topological charge density to the bulk spectral asymmetry, we treat the instanton ensemble as a ”Villani gas” evolving under an effective kinetic equation. Crucially, we argue that the instanton gas undergoes an entropy-driven relaxation gov- erned by quantum hypocoercivity. Within the proposed effective framework, we argue that a spectral gap in the instanton collision operator provides a candidate geometric mechanism for the emergence of the macroscopic Yang-Mills mass gap (ΛQCD), protected by the zero- index condition of the Atiyah-Patodi-Singer theorem. Finally, we propose a holographic interpretation of the Witten-Veneziano relation, in which the topological susceptibility χt of four-dimensional spacetime is constrained by the spectral geometry of the extra dimensions.

@article{deceuster2026_87-investigations-in,
  title = {Investigations into an Unobserved Photonic Law of Nature (Paper VI): Holographic Protection of Non-Abelian Sectors — Hypocoercivity, Instanton Gases, and the QCD Mass Gap},
  author = {De Ceuster, Peter},
  year = {2026},
  month = {02},
  institution = {SIG Labs},
  doi = {10.5281/zenodo.21599631},
  url = {https://peterdeceuster.uk/papers/87-investigations-into-an-unobserved-photonic-law-of-nature},
  note = {Full text available at https://peterdeceuster.uk/articenter/work/six.pdf}
}