{"paper":{"title":"All-loop geometry for four-point correlation functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Chia-Kai Kuo, Song He, Yu-tin Huang","submitted_at":"2024-05-30T17:42:17Z","abstract_excerpt":"In this letter, we consider a positive geometry conjectured to encode the loop integrand of four-point stress-energy correlators in planar $\\mathcal{N}=4$ super Yang-Mills. Beginning with four lines in twistor space, we characterize a positive subspace to which an $\\ell$-loop geometry is attached. The loop geometry then consists of $\\ell$ lines in twistor space satisfying positivity conditions among themselves and with respect to the base. Consequently, the $\\textit{loop geometry}$ can be viewed as fibration over a $\\textit{tree geometry}$. The fibration naturally dissects the base into chambe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.20292","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2405.20292/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}