{"schema":"pubphys.bundle/1","record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"12d9b4eebbc1fe90faef7a27f5b27cc9a4efc4e2b507e72925e0a8584864ac26","created":"2026-10-15T23:43:22Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["095b70ae81631d849cfcc9cf8ab295b6f7ce78510af1bfcb4f6a47fcc56b83d8","ce59fb6cd812fc05906d0c60a71c75ea22bc686bcf38e7c3ef7010834d98ee7b"],"salt":"1fb41706b4b32fd810b38e27edb77eaf9b7ad682c984a38b5d986703dd205e77","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":"2","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, $\\sin(\\pi k/N)/\\sin(\\pi/N)$), or follow neither form.","problem_ref":"095b70ae81631d849cfcc9cf8ab295b6f7ce78510af1bfcb4f6a47fcc56b83d8","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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