{"schema":"pubphys.bundle/1","record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"1e7aaa8c560621c0b6a2b665b1d75ffb61fc44c50ee6eb68955d6cade25b4eb2","created":"2026-10-03T07:18:08Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"8ab97c3a5459cd96dc2109688889a76d12c8367900205c24f14f3626b81e5dbe","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"value","assisted_by":[],"external_id":"qft.confinement.k-string-tensions","kind":"well-posed","literature_status":"open","n":"1","parents":[],"plain":"Heavy test charges can be grouped by how many units k of a color charge they carry that cannot be cancelled by gluons, and each k is joined by a flux string of different tension. The exact rule giving these tensions for many colors is unknown.","posed_since":"","precise":"In $4\\mathrm{D}$ $\\mathrm{SU}(N)$ Yang-Mills let $\\sigma_k$ be the asymptotic string tension between static sources of N-ality k. Determine $\\sigma_k/\\sigma_1$ at large N, in particular whether corrections to the free-string value k are of order $1/N$ (Casimir scaling, $k(N-k)/(N-1)$) or of order $1/N^{2}$ (sine law, $\\operatorname{sin}(\\pi k/N)/\\operatorname{sin}(\\pi/N)$), or follow neither form.","problem_ref":null,"references":"","settled_by":"Large-$N$ extrapolation of continuum lattice $\\sigma_{k}$ for $N$ up to 8 or more, or an analytic large-$N$ derivation of the ratio.","status_note":"Lattice data in $3+1$ dimensions for $N$ up to about 8 lie between Casimir scaling and the sine law without separating $1/N$ from $1/N^{2}$ corrections; in $2+1$ dimensions the leading correction was found to be of order $1/N$ (Athenodorou and Teper 2016).","title":"Ratio of k-string tensions in large-N Yang-Mills 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