Structural Parallels Between Spectral Confinement on SU(2) and the Yang–Mills Mass Gap: A Conjecture Programme

Paper 15 in The Geometry of the Critical Line programme. We identify structural parallels between the spectral geometry of the compact group manifold SU(2) ≅ S³ and the Yang–Mills mass gap problem. The Laplace–Beltrami operator on S³ has a purely discrete spectrum with explicit eigenvalues λ_l = l(l+2)/R² and a positive spectral gap λ₁ = 3/R². In temporal gauge, the Yang–Mills Hamiltonian restricted to spatially constant gauge fields reduces to this Laplacian, so the geometric gap is a necessary condition for any spectral gap in the full quantum theory. The naive infinite-volume limit R → ∞ sends this gap to zero; the physical mass gap emerges from dimensional transmutation, not from the classical geometry…