What question did this study set out to answer?

The aim is to calculate the SU(2) Yang–Mills mass gap on the Poincaré homology sphere.

February 5, 2026Open Access

Yang–Mills Mass Gap on the Poincaré Homology Sphere

Puntos clave

The aim is to calculate the SU(2) Yang–Mills mass gap on the Poincaré homology sphere.
Utilized Weitzenböck curvature to establish a curvature floor.
Applied topological vacuum isolation to identify isolated flat connections.
Conducted spectral computation via the McKay correspondence for the extended E₈ diagram.
Established a baseline mass gap of Δ² = 4/R².
Identified a ninefold enhancement of the gap, Δ² = 36/R², due to icosahedral filtering.
Confirmed that the existence of the gap is topological and its numerical value varies with the metric.

Resumen

We compute the SU(2) Yang–Mills mass gap on the Poincaré homology sphere S³/2I, where 2I is the binary icosahedral group of order 120. Three independent arguments establish the result: a Weitzenböck curvature floor (λ ≥ 2/R²), topological vacuum isolation (three isolated flat connections with vanishing H¹), and explicit spectral computation via the McKay correspondence for the extended E₈ diagram. The Galois conjugate vacuum exhibits a ninefold enhancement (Δ² = 36/R²) over the baseline gap (Δ² = 4/R²), arising from icosahedral filtering of the first four coexact levels. The existence of the gap is topological; its numerical value is metric-dependent.

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