{"paper":{"title":"Biadjoint scalar tree amplitudes and intersecting dual associahedra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Hadleigh Frost","submitted_at":"2018-02-09T18:46:36Z","abstract_excerpt":"We present a new formula for the biadjoint scalar tree amplitudes $m(\\alpha|\\beta)$ based on the combinatorics of dual associahedra. Our construction makes essential use of the cones in 'kinematic space' introduced by Arkani-Hamed, Bai, He, and Yan. We then consider dual associahedra in 'dual kinematic space.' If appropriately embedded, the intersections of these dual associahedra encode the amplitudes $m(\\alpha|\\beta)$. In fact, we encode all the partial amplitudes at $n$-points using a single object (a fan) in dual kinematic space. Equivalently, as a pleasant corollary of our construction, a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.03384","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":""},"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"}