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Mass Gap of Lattice Yang--Mills Theory up to the Dobrushin Ceiling

Contributed by Deep Bhattacharjee, Ushashi Bhattacharya

We prove that the Hessian of the Wilson action on $d$ -dimensional lattice gauge fields is bounded by $4d$ , sharply, so lattice $\SU(N)$ Yang--Mills theory has a unique infinite-volume state with a positive mass gap for $|\beta|<1/(8d)$ . Every von Mises--Fisher law on the three-sphere moves by at most a quarter of its parameter in Kantorovich distance; consequently four-dimensional $\SU(2)$ theory has a mass gap for $\beta_W<2/9$ , the ceiling of all single-link Dobrushin arguments. A gauge-invariant finite-box criterion for decay and the area law is also given. The continuum mass gap remains open.

A mix of human-written and AI-generated textHuman understanding: some partsBakry-Emery curvatureDobrushin uniquenessKantorovich distancelattice gauge theorymass gapvon Mises-Fisher law

Oct 18, 2026PDF ↗View work →

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Mass Gap of Lattice Yang--Mills Theory up to the Dobrushin Ceiling

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