{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"75900429a4f2a7641313cff7fe11eab2a83b37c546b33fe8a00f5d3c78101aee","created":"2026-10-03T07:18:08Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"676fcfafcf2579bdd756d8a1d009b514fc8d3612ff47d9134f80d7fc7a0d84c5","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"value","assisted_by":[],"external_id":"qft.cft-rg.su3-conformal-window","kind":"well-posed","literature_status":"contested","n":"1","parents":[],"plain":"QCD with many massless quark species becomes scale invariant at long distances. The smallest number of species for which this happens is unknown.","posed_since":"","precise":"$\\mathrm{SU}(3)$ gauge theory with $N_{f}$ massless Dirac fermions in the fundamental representation is asymptotically free for $N_{f} < 16.5$ and has a perturbative IR fixed point near that value. Determine $N_{f}^{*}$ such that for $N_{f}^{*} \\le N_{f} < 16.5$ the IR is a CFT and for smaller $N_{f}$ chiral symmetry breaks; in particular decide $N_{f} = 8, 10 \\text{ and } 12$.","problem_ref":null,"references":"","settled_by":"Continuum-extrapolated lattice determinations of the step-scaling function or spectrum for $N_f = 8\\ \\text{to}\\ 13$ that agree between independent groups.","status_note":"Lattice groups disagree on $N_{f} = 10\\text{ and }12$; estimates of $N_{f}^{*}$ range from about 9 to 13 (2009-2025).","title":"Lower edge of the conformal window in SU(3) gauge theory","topic_ref":"59b3cca1f32dc01e525b6517c866b60ced9512aa01bc51694ea2f6fc00c1ca06"},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"71f104c54df89ac7e8dcfd60b9073ed47f8980f93ba312ff887d7cb64b4fa66b","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"451c73f37287398c07e2a5f29b34e886f6b330d4ea64349e573bfe6595951733","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"164Enop8Of0zFvT7usQ2b2LE5-VAi0mLzTgWJHTc2UyXxiZdheWwYrC-LEMoR3Ye5so_sMo0zvDfymyjfUN5Dw"},"schema":"pubphys.envelope/1"},"record_hash":"71f104c54df89ac7e8dcfd60b9073ed47f8980f93ba312ff887d7cb64b4fa66b","leaf_index":1896}