{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"962030b661ecc51244c92e59f8e1b952a8874ea300c8fdfd2ea6c20fc4d7ebd8","created":"2026-10-03T07:18:09Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"a50926e5c93ac699e972a21f2cd6c4b4ccc65c8a75934f3c8817b5502892eeac","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"yes-no","assisted_by":[],"external_id":"qft.rg-irreversibility.scale-vs-conformal","kind":"well-posed","literature_status":"partially-resolved","n":"1","parents":[],"plain":"A theory that looks the same at all magnifications usually has a larger symmetry, conformal symmetry. Whether this always holds in four dimensions is not proven.","posed_since":"1988","precise":"For a unitary, Poincare-invariant 4D QFT with a well-defined stress tensor, determine whether scale invariance implies conformal invariance nonperturbatively. It is proven in 2D (Polchinski 1988), shown to all orders of perturbation theory in 4D (Luty, Polchinski, Rattazzi; Fortin, Grinstein, Stergiou, 2012), and argued nonperturbatively under assumptions (Dymarsky, Komargodski, Schwimmer, Theisen 2013).","problem_ref":null,"references":"","settled_by":"A nonperturbative argument without extra assumptions, or a unitary scale-invariant but non-conformal 4D theory.","status_note":"Proven to all orders in perturbation theory (2012) and nonperturbatively under extra assumptions (2013); no general proof.","title":"Does scale invariance imply conformal invariance in four dimensions","topic_ref":"aa2c9297ee0f9c5637717e0362dc66e39fae921c636c489893e101ec3f0ff180"},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"fc66f564ad4a781eca2271647d28088bdd6aa6796837ca4a8b10003e448f42da","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"0839ceb75e9c3cf55eb45884d1b565fc9a7bf32fa692c238cfb2e27733378f08","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"alEUi71S0kv4Wj-z_gUGj8DRMoM4CQNVz2Nnqa5wqlAIBxmaN5LOEVGtdyfH9-t2VdvXY6njMs-GCq78wIg5CA"},"schema":"pubphys.envelope/1"},"record_hash":"fc66f564ad4a781eca2271647d28088bdd6aa6796837ca4a8b10003e448f42da","leaf_index":1945}