Geometric Stabilization of the Yang-Mills Vacuum: A Derivation of the Mass Gap via Non-Associative Stiffness

We propose a rigorous geometric mechanism for the origin of the mass gap in non-
Abelian gauge theories, derived from the topological constraints of M-theory compactified on
manifolds of G2 holonomy. We demonstrate that the vacuum of Quantum Chromodynamics
(QCD) is not a passive stage but a dynamical medium governed by a “Geometric Stiffness”
parameter, βQCD = 6/π ≈ 1.91. This parameter arises from the ratio of the non-associative
bulk degrees of freedom to the associative measure of the stability cycle. By modifying the
equation of state for the effective string description of color flux tubes, we introduce the
Wolf-Toffoletto-Schutza (WTS) action, which incorporates this super-linear stiffness.
We establish a formal duality between the Lagrangian configuration space of high-β
magnetospheric plasma filaments and the color flux tubes of the strong interaction. Uti-
lizing the Thin Filament Code (TFC) as a non-perturbative solver, we demonstrate that
the super-linear restoring force (Γef f ≈ 2.91) forbids zero-energy excitations, generating a
strictly positive fundamental frequency ω0 > 0. The resulting spectrum predicts a scalar
glueball mass of 1710 MeV and resolves the Proton Spin Crisis with a predicted quark spin
contribution of Σ ≈ 0.34, matching experimental data. This work offers an effective field
theory description of confinement rooted in the non-associative geometry of the vacuum.