{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:CDYBTOLAIG7CGQZ3K7Q5PYKBRJ","short_pith_number":"pith:CDYBTOLA","schema_version":"1.0","canonical_sha256":"10f019b96041be23433b57e1d7e1418a659eb1324ed6378be80d4f6f1d938fdc","source":{"kind":"arxiv","id":"1204.5221","version":2},"attestation_state":"computed","paper":{"title":"The $a$-theorem and the Asymptotics of 4D Quantum Field Theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Joseph Polchinski, Markus A. Luty, Riccardo Rattazzi","submitted_at":"2012-04-23T22:24:57Z","abstract_excerpt":"We study the possible IR and UV asymptotics of 4D Lorentz invariant unitary quantum field theory. Our main tool is a generalization of the Komargodski-Schwimmer proof for the $a$-theorem. We use this to rule out a large class of renormalization group flows that do not asymptote to conformal field theories in the UV and IR. We show that if the IR (UV) asymptotics is described by perturbation theory, all beta functions must vanish faster than $(1/|\\ln\\mu|)^{1/2}$ as $\\mu \\to 0$ ($\\mu \\to \\infty$). This implies that the only possible asymptotics within perturbation theory is conformal field theor"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1204.5221","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2012-04-23T22:24:57Z","cross_cats_sorted":[],"title_canon_sha256":"52556aca97644e788bb3b1141f8ace24fec3e4907e37fb2c295df1b004a34a1a","abstract_canon_sha256":"bdb1a9d1bf9e84a2b0c5bdbb1f69bdcdcf98751a4a3c2164e4b986fb8e70e575"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:57:47.051883Z","signature_b64":"vB1wvoia7MGNX8vn+bivZzNDt06Ft5PWeER0pScXITaDMLasuubXelQcOuhO/b6+ntHncUTnAmCI+shkrcOnDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"10f019b96041be23433b57e1d7e1418a659eb1324ed6378be80d4f6f1d938fdc","last_reissued_at":"2026-05-18T01:57:47.051117Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:57:47.051117Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The $a$-theorem and the Asymptotics of 4D Quantum Field Theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Joseph Polchinski, Markus A. Luty, Riccardo Rattazzi","submitted_at":"2012-04-23T22:24:57Z","abstract_excerpt":"We study the possible IR and UV asymptotics of 4D Lorentz invariant unitary quantum field theory. Our main tool is a generalization of the Komargodski-Schwimmer proof for the $a$-theorem. We use this to rule out a large class of renormalization group flows that do not asymptote to conformal field theories in the UV and IR. We show that if the IR (UV) asymptotics is described by perturbation theory, all beta functions must vanish faster than $(1/|\\ln\\mu|)^{1/2}$ as $\\mu \\to 0$ ($\\mu \\to \\infty$). This implies that the only possible asymptotics within perturbation theory is conformal field theor"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.5221","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1204.5221","created_at":"2026-05-18T01:57:47.051220+00:00"},{"alias_kind":"arxiv_version","alias_value":"1204.5221v2","created_at":"2026-05-18T01:57:47.051220+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.5221","created_at":"2026-05-18T01:57:47.051220+00:00"},{"alias_kind":"pith_short_12","alias_value":"CDYBTOLAIG7C","created_at":"2026-05-18T12:27:01.376967+00:00"},{"alias_kind":"pith_short_16","alias_value":"CDYBTOLAIG7CGQZ3","created_at":"2026-05-18T12:27:01.376967+00:00"},{"alias_kind":"pith_short_8","alias_value":"CDYBTOLA","created_at":"2026-05-18T12:27:01.376967+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":8,"internal_anchor_count":6,"sample":[{"citing_arxiv_id":"2605.21326","citing_title":"Matching $A$ with $F$ in long-range QFTs","ref_index":13,"is_internal_anchor":true},{"citing_arxiv_id":"2605.22919","citing_title":"Scale-Invariant Open Quantum Systems","ref_index":19,"is_internal_anchor":true},{"citing_arxiv_id":"2406.19441","citing_title":"Moduli Spaces in CFT: Large Charge Operators","ref_index":18,"is_internal_anchor":true},{"citing_arxiv_id":"2605.21326","citing_title":"Matching $A$ with $F$ in long-range QFTs","ref_index":13,"is_internal_anchor":true},{"citing_arxiv_id":"2605.21326","citing_title":"Matching $A$ with $F$ in long-range QFTs","ref_index":13,"is_internal_anchor":true},{"citing_arxiv_id":"2509.18255","citing_title":"Bootstrapping transport in the Drude-Kadanoff-Martin model","ref_index":40,"is_internal_anchor":true},{"citing_arxiv_id":"2604.15420","citing_title":"Local CFTs extremise $F$","ref_index":25,"is_internal_anchor":false},{"citing_arxiv_id":"2604.15445","citing_title":"Universal Description of Decoherence in Scale-Invariant Environments","ref_index":6,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/CDYBTOLAIG7CGQZ3K7Q5PYKBRJ","json":"https://pith.science/pith/CDYBTOLAIG7CGQZ3K7Q5PYKBRJ.json","graph_json":"https://pith.science/api/pith-number/CDYBTOLAIG7CGQZ3K7Q5PYKBRJ/graph.json","events_json":"https://pith.science/api/pith-number/CDYBTOLAIG7CGQZ3K7Q5PYKBRJ/events.json","paper":"https://pith.science/paper/CDYBTOLA"},"agent_actions":{"view_html":"https://pith.science/pith/CDYBTOLAIG7CGQZ3K7Q5PYKBRJ","download_json":"https://pith.science/pith/CDYBTOLAIG7CGQZ3K7Q5PYKBRJ.json","view_paper":"https://pith.science/paper/CDYBTOLA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1204.5221&json=true","fetch_graph":"https://pith.science/api/pith-number/CDYBTOLAIG7CGQZ3K7Q5PYKBRJ/graph.json","fetch_events":"https://pith.science/api/pith-number/CDYBTOLAIG7CGQZ3K7Q5PYKBRJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CDYBTOLAIG7CGQZ3K7Q5PYKBRJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CDYBTOLAIG7CGQZ3K7Q5PYKBRJ/action/storage_attestation","attest_author":"https://pith.science/pith/CDYBTOLAIG7CGQZ3K7Q5PYKBRJ/action/author_attestation","sign_citation":"https://pith.science/pith/CDYBTOLAIG7CGQZ3K7Q5PYKBRJ/action/citation_signature","submit_replication":"https://pith.science/pith/CDYBTOLAIG7CGQZ3K7Q5PYKBRJ/action/replication_record"}},"created_at":"2026-05-18T01:57:47.051220+00:00","updated_at":"2026-05-18T01:57:47.051220+00:00"}