{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"91d9c471df07e8f516e0cc603b834a3571e8379aa2c7d77125b48b714473b5eb","created":"2026-10-15T23:43:22Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["ce59fb6cd812fc05906d0c60a71c75ea22bc686bcf38e7c3ef7010834d98ee7b","fc66f564ad4a781eca2271647d28088bdd6aa6796837ca4a8b10003e448f42da"],"salt":"3abcd229469beba33830aac694823fed238030d53ab89e108f13ded75f0e76b9","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":"2","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":"fc66f564ad4a781eca2271647d28088bdd6aa6796837ca4a8b10003e448f42da","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":null},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"d31731e026d29b768edfec20be22e699fb895a5eac1c4311fac830d4a328b6fb","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"de816eeea31819d905b23cde6b5e2a522200413b76a46d5d5c625aa27148d012","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"C0geVKxKoD92x1qN7JMGuuc_KvvcE_DwcOJYUfWHxOK0BPLwOhYpEoF_3YuHzkP53kYLyUkh13verDZX3pSyCQ"},"schema":"pubphys.envelope/1"},"record_hash":"d31731e026d29b768edfec20be22e699fb895a5eac1c4311fac830d4a328b6fb","leaf_index":3670}