{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"46f2c283bdc485fab4644d95e47e22e5f7f2f4a241c82af554ab9c2975f7c349","created":"2026-10-03T07:18:09Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"d28c4b09e6cd4f8f36863453b2aa4b460db16d1a945a41a93344d264a28edee6","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"yes-no","assisted_by":[],"external_id":"qft.rg-irreversibility.f-theorem-5d","kind":"well-posed","literature_status":"open","n":"1","parents":[],"plain":"In three dimensions, a number computed by placing the theory on a sphere is proven to drop under coarse-graining (the F-theorem). Whether the analogous number drops in five dimensions is unknown.","posed_since":"2010","precise":"For a unitary $d$-dimensional CFT define F~ = sin(pi d/2) log $Z$(S^d), with Z the renormalized partition function on the round sphere (Giombi and Klebanov 2014); in $d = 5$ this is F~ = log Z(S^5). Prove or refute F~_UV > F~_IR for every unitary RG flow between 5D CFTs. The 3D case was proven from strong subadditivity of entanglement entropy (Casini and Huerta 2012); that argument has not been extended to $d = 5$.","problem_ref":null,"references":"","settled_by":"A general proof for unitary $5\\mathrm{D}$ flows, or a unitary $5\\mathrm{D}$ flow (for example a $5\\mathrm{D}$ SCFT deformed into a gauge theory) with F~_UV <= F~_IR.","status_note":"Consistent with free-field, large-N and $\\epsilon$-expansion examples (2014 onward); no general proof as of 2026.","title":"Does the sphere free energy decrease along five-dimensional RG flows","topic_ref":"aa2c9297ee0f9c5637717e0362dc66e39fae921c636c489893e101ec3f0ff180"},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"8cfb212400e48962cc9bb94aa661245796414c71fd045c38f3475886a87e7729","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"a98fe3239dc2697df5ddcd43b1aa17827b91829b76191de0d993e87c95bea0dc","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"ubLZyDckypWGbSJVAJmnVHA1he6abVv-u1nRoSEZI4FrB5j6COYn3PwbNc28LkBMMevaPpV0e7fWVRVAwNLnCg"},"schema":"pubphys.envelope/1"},"record_hash":"8cfb212400e48962cc9bb94aa661245796414c71fd045c38f3475886a87e7729","leaf_index":1944}