{"paper":{"title":"From Physics to Number Theory via Noncommutative Geometry, Part II: Renormalization, the Riemann-Hilbert correspondence, and motivic Galois theory","license":"","headline":"","cross_cats":["math-ph","math.AG","math.MP","math.NT","math.QA"],"primary_cat":"hep-th","authors_text":"Alain Connes (College de France), Matilde Marcolli (MPIM)","submitted_at":"2004-11-11T08:49:17Z","abstract_excerpt":"We establish a precise relation between Galois theory in its motivic form with the mathematical theory of perturbative renormalization (in the minimal subtraction scheme with dimensional regularization). We identify, through a Riemann-Hilbert correspondence based on the Birkhoff decomposition and the t'Hooft relations, a universal symmetry group (the \"cosmic Galois group\" suggested by Cartier), which contains the renormalization group and acts on the set of physical theories. This group is closely related to motivic Galois theory. We construct a universal singular frame of geometric nature, in"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/0411114","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/hep-th/0411114/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"}