Non-Perturbative Spectral Gaps in SU (N ) Yang-Mills Theory via Hyper-Holonomic Renormalization Group Flows

Mathematical Applications of Science Fiction We present a rigorous derivation of the mass gap in purenon-abelian Yang-Mills theory on R4 with gauge groupG = SU (N ). By constructing a hyper-holonomic spectralsequence over the moduli space of irreducible connectionsA/G, we circumvent the Gribov ambiguity inherent in theFaddeev-Popov quantization. We introduce a novel Void-Operator Expansion (VOE) that regularizes the ultravioletdivergence without breaking gauge invariance, mappingthe continuum theory to a convergent sequence of Sobolev-Hilbert spaces. We prove, via a transfinite induction on thecluster expansion of the Wilson loops, that the spectrumof the Hamiltonian H is bounded from below by ∆ > 0 forthe first excited state. This establishes the existence of amassive glueball state in the continuum limit, satisfying theWightman axioms.