{"paper":{"title":"Differential Space of Feynman Integrals: Annihilators and $\\mathcal{D}$-module","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["hep-ph","math-ph","math.MP"],"primary_cat":"hep-th","authors_text":"Nobuki Takayama, Pierpaolo Mastrolia, Saiei-Jaeyeong Matsubara-Heo, Vsevolod Chestnov, William J. Torres Bobadilla, Wojciech Flieger","submitted_at":"2025-06-12T08:04:44Z","abstract_excerpt":"We present a novel algorithm for constructing differential operators with respect to external variables that annihilate Feynman-like integrals and give rise to the associated $\\mathcal{D}$-modules, based on Griffiths-Dwork reduction. By leveraging the Macaulay matrix method, we derive corresponding relations among partial differential operators, including systems of Pfaffian equations and Picard-Fuchs operators. Our computational approach is applicable to twisted period integrals in projective coordinates, and we showcase its application to Feynman graphs and Witten diagrams. The method yields"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.10456","kind":"arxiv","version":1},"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/2506.10456/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"}