{"paper":{"title":"Consistency Relation for Fixed Point Dynamics","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["hep-th"],"primary_cat":"hep-ph","authors_text":"Alan Pinoy, Francesco Sannino, Oleg Antipin, Shahram Vatani","submitted_at":"2025-04-08T12:50:27Z","abstract_excerpt":"We gain insight on the fixed point dynamics of $d$ dimensional quantum field theories by exploiting the critical behavior of the $d-\\epsilon$ sister theories. To this end we first derive a self-consistent relation between the $d-\\epsilon$ scaling exponents and the associated $d$ dimensional beta functions. We then demonstrate that to account for an interacting fixed point in the original theory the related $d-\\epsilon$ scaling exponent must be multi-valued in $\\epsilon$. We elucidate our findings by discussing several examples such as the QCD Banks-Zaks infrared fixed point, QCD at large numbe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.05988","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/2504.05988/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"}