{"schema":"pubphys.bundle/1","record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"edfbcf75dc33e389ef732a113b788263a1cf3aac829346c2e26911cf50e95395","created":"2026-10-03T07:18:09Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"21cc8586356084594cdc9088a973ebb9003983c193a027b79314414ab7369e3e","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"yes-no","assisted_by":[],"external_id":"qft.positive-geometry.yang-mills-integrand","kind":"well-posed","literature_status":"open","n":"1","parents":[],"plain":"For gluons without supersymmetry, a 2024 construction using curves drawn on surfaces gives a natural loop integrand (the function integrated over loop momenta) in the limit of many colors. Whether it is the volume-like form of an actual geometric shape is not known.","posed_since":"","precise":"Arkani-Hamed, Cao, Dong, Figueiredo and He (Phys. Rev. Lett. 134, 171601, 2025) defined a gauge-invariant, cut-consistent planar (leading-color) Yang-Mills loop integrand using surface kinematics, building on curve-integral formulas for $\\operatorname{Tr}\\phi^{3}$ theory, with explicit results at one loop for all multiplicities and a simplest two-loop case. Determine whether this integrand, for all multiplicities n and loop orders L in the planar limit, is the canonical form of a positive geometry, and whether a 4D helicity-basis version exists.","problem_ref":null,"references":"","settled_by":"Construction of a positive geometry with this canonical form, or a proof that the integrand has non-logarithmic singularities incompatible with one.","status_note":"The planar integrand was defined in 2024 (published 2025); no positive geometry with this canonical form is known as of 2026.","title":"Geometric origin of the non-supersymmetric Yang-Mills loop 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