{"schema":"pubphys.bundle/1","record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"fab8b916e4732cf31e62901ac023ac962ac9d61e06619ab6b498722e8ec1e8b8","created":"2026-10-03T07:18:06Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011","75b7b83537c0f3d60e2005415e11f4bb54b1f3dceca46a614d549cae347dca99"],"salt":"33b126c0c61f7dfac71515e0d9a303910dcfa835bce7f7789ad42f02c011aabe","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"proof","assisted_by":[],"external_id":"mathph.yang-mills.continuum-limit-4d","kind":"well-posed","literature_status":"open","n":"1","parents":[{"note":"","parent_revision":"75b7b83537c0f3d60e2005415e11f4bb54b1f3dceca46a614d549cae347dca99","relation":"special_case"}],"plain":"Yang-Mills theory can be defined on a grid of points, and the task is to show that it has a sensible limit as the grid spacing goes to zero. The limit should be interacting, not a free theory.","posed_since":"","precise":"Take $\\mathrm{SU}(N)$ lattice gauge theory with the Wilson action on $(\\epsilon \\mathrm{Z})^4$, with bare coupling chosen by asymptotic freedom, $g(\\epsilon)^2 \\sim 1/(2 b_0 \\operatorname{log}(1/(\\epsilon \\Lambda)))$ with $b_0 = 11 N/(48 \\pi^2)$, i.e. $1/g^2 \\sim (11 N/(24 \\pi^2)) \\operatorname{log}(1/(\\epsilon \\Lambda))$. Prove that correlations of gauge-invariant observables (smoothed Wilson loops or smeared $F^2$) converge as $\\epsilon \\to 0$ in infinite volume to a non-Gaussian limit satisfying the Osterwalder-Schrader axioms. Answer: a proof.","problem_ref":null,"references":"","settled_by":"A rigorous renormalization-group or probabilistic proof of the infinite-volume continuum limit with non-Gaussian correlations.","status_note":"Balaban's renormalization-group program of the 1980s gave ultraviolet stability bounds in finite volume but did not complete the construction.","title":"Continuum limit of four-dimensional lattice Yang-Mills 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