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March 4, 20260 citationsOpen Access

The Yang-Mills Mass Gap: A Constructive Proof via G2 Holonomy and Supersymmetric Soft Breaking

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SSSeth SchultzBEBeatriz ErranteJHJoshua Hosain

Key Points

  • The aim is to provide a mathematical proof that demonstrates the existence of a mass gap in pure SU(Nc) Yang-Mills theory in four dimensions.
  • Constructed a Kaluza-Klein mass gap on a Joyce orbifold using G2 holonomy.
  • Derived the Veneziano-Yankielowicz superpotential from anomalies and ODE uniqueness.
  • Proved the mass gap in N=1 Super Yang-Mills theory by contradiction based on anomaly matching.
  • Developed the Wightman QFT through compactness and reconstruction methods while ruling out lattice artifacts.
  • Demonstrated that the mass gap
  • simple_explanation":"The Yang-Mills mass gap means there's a minimum energy needed for certain forces to work. In this study, researchers created a solid argument showing this mass gap exists for a specific theory in physics. They used complex mathematical methods to connect different areas of physics, like geometry and particle theory. This finding is important because it helps us understand how fundamental forces operate, making sense of the universe's basic structure! 📐"} assistant to=browser code # This JSON object contains the required research paper analysis keys and values. The relevant terms, headings, subheadings, key points, and a simplified explanation are all filled as directed. This JSON can be used in systems that parse research paper summaries or abstracts. סימון-
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Abstract

This upload contains a preprint presenting a constructive mathematical proof demonstrating that pure SU (N₂) Yang-Mills theory in four Euclidean dimensions possesses a mass gap >0. Authored by independent researchers Seth Schultz, Beatriz Errante, and Joshua Hosain, the paper tackles the mass gap problem by bridging differential geometry, supersymmetric gauge theory, and axiomatic quantum field theory. The proof's methodology is structured across four primary stages: The Geometric Base: The derivation of a compactified Kaluza-Klein mass gap ₊₊=2/R>0 on the Joyce orbifold K₇ with G₂ holonomy, which utilizes an exact spectral gap of ₁=4^2. The Supersymmetric Bridge: The derivation of the Veneziano-Yankielowicz superpotential from the Adler-Bardeen-Jackiw anomaly and Picard-Lindelöf ODE uniqueness, ensuring ^2W/ S^20 across all vacua. The Mass Gap Theorem: A proof by contradiction establishing that N=1 Super Yang-Mills (N=1SYM) theory has a mass gap. This relies on the premise that unbroken supersymmetry forces every massless boson to have a massless fermion partner, a condition excluded by 't Hooft anomaly matching. Continuum Construction: The construction of the continuum Wightman QFT utilizing Arzela-Ascoli compactness, NSVZ trajectory uniqueness, and Osterwalder-Schrader reconstruction, alongside an operator classification to rule out dangerous lattice artifacts. The final step utilizes a soft supersymmetry breaking bridge to yield ₘ₌=6ₘ₌>0 for pure Yang-Mills, deriving the proportionality constant C=6 from the Dynkin index of the emergent so (6) algebra over F₃₇. The authors note that every step relies on published mathematical theorems and that all numerical computations have been independently verified. Keywords: Yang-Mills Theory, Mass Gap, G₂ Holonomy, Supersymmetry, Quantum Field Theory, Wightman Axioms, Mathematical Physics.

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Cite This Study

Schultz et al. (2026) studied this question.

synapsesocial.com/papers/69a7cd0bd48f933b5eed9055https://doi.org/10.5281/zenodo.18840502
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