The 0⁺⁺ Glueball as a Topological Defect on S⁸

This preprint presents a novel geometric model of the Yang–Mills mass gap. We propose that the 0⁺⁺ glueball is not a free harmonic, but the pinned ground state of the S⁸ vacuum in the presence of a topological defect (a “knot” classified by π₇(S⁷) ≅ ℤ).

This defect, modeled as a point interaction (a self-adjoint extension), forces the vacuum into a new ground state, creating a positive mass gap λ₁ > 0. We then conjecture that this defect is self-resonant, forcing the entire tower of its quantized vibrations (ℓ = 2, 3, …) to align with the free S⁸ manifold’s spectrum: λ_ℓ = ℓ(ℓ + 7)/R².

This “self-holographic” model provides a physical mechanism for the mass gap. After fixing the overall scale with the m₁ state, the model yields a tower of parameter-free mass ratios in strong agreement with lattice QCD data. The work connects spectral geometry, topological defects, and the origin of the mass gap.