{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"bfd3d9897c8a2405304af9c3eea4859d240298f5076678777bdf1f21bd32c333","created":"2026-10-15T23:43:22Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["ce59fb6cd812fc05906d0c60a71c75ea22bc686bcf38e7c3ef7010834d98ee7b","e24ea3d72177667230f744fc7d85fc22ce620b754bd3f2b083425676f0ea4b8d"],"salt":"e8ac026b22490354b5f620cff260fb71b4fbc174bf39232370697e63993bd6a3","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":"2","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":"e24ea3d72177667230f744fc7d85fc22ce620b754bd3f2b083425676f0ea4b8d","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":null},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"4bf5b457c3879220d1670fc6fbdfb54daf7c30d5d9299c545fa7b08a75436bd8","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"4312ece75ec2c6d5616e609aab256c975fed588b1ad259acd172e9f57b7b18ea","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"qUyh31o6XC3EQ-2wUyw3BF1NcpS4AA4wlrfduAYIzrOtvmx6sYvDAw3vBPA8Q2EuLIi1VRTLQcQzudDXsAgiAQ"},"schema":"pubphys.envelope/1"},"record_hash":"4bf5b457c3879220d1670fc6fbdfb54daf7c30d5d9299c545fa7b08a75436bd8","leaf_index":3672}