{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"67af0810bb15d9244ccd18cdff9ba548fa5c9fcffa13c57cad1f4b3a98a8738f","created":"2026-10-03T07:18:09Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"72463e2cf7326fdb6ae299a2039126a3956be496670eb9f23f7be6fad5cf5cbe","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"yes-no","assisted_by":[],"external_id":"qft.rg-irreversibility.six-d-a-theorem","kind":"well-posed","literature_status":"partially-resolved","n":"1","parents":[],"plain":"In two and four dimensions a number counting effective degrees of freedom is proven to drop under coarse-graining. In six dimensions this is proven only for special supersymmetric cases.","posed_since":"1988","precise":"In unitary 6D QFT, the Euler coefficient a of the trace anomaly is conjectured to satisfy $a_{UV} > a_{IR}$ for every RG flow between CFTs. The 4D dilaton proof (Komargodski and Schwimmer 2011) does not carry over because the relevant six-derivative dilaton coupling is not sign-definite by unitarity. Prove or refute the inequality for general, including non-supersymmetric, flows.","problem_ref":null,"references":"","settled_by":"A general argument (dilaton, entanglement or other) establishing $a_{\\mathrm{UV}} > a_{\\mathrm{IR}}$ in $d = 6$, or a unitary flow with $a_{\\mathrm{UV}} \\le a_{\\mathrm{IR}}$.","status_note":"Proven for supersymmetric tensor-branch flows and, in 2023-2025, orbi-instanton Higgs-branch flows; open in general.","title":"Does the a-anomaly decrease along all six-dimensional RG flows","topic_ref":"aa2c9297ee0f9c5637717e0362dc66e39fae921c636c489893e101ec3f0ff180"},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"e24ea3d72177667230f744fc7d85fc22ce620b754bd3f2b083425676f0ea4b8d","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"b044c92772f08217e34a170a11c02969339a96daae53b625531e132636fb200b","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"eRObdhWDqGITD04EnTwy4AwGVrpmEjDY9JhGqsCyiKayKR9CsX0L-P4sqvzITOK2zxnLp48jgn6v76SViVk6Dg"},"schema":"pubphys.envelope/1"},"record_hash":"e24ea3d72177667230f744fc7d85fc22ce620b754bd3f2b083425676f0ea4b8d","leaf_index":1946}