{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"22b02dc8a24181efd5a3b0cc07b4ccd583fb71c149bf7b8718eb306161f50573","created":"2026-10-15T23:43:22Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["8cfb212400e48962cc9bb94aa661245796414c71fd045c38f3475886a87e7729","ce59fb6cd812fc05906d0c60a71c75ea22bc686bcf38e7c3ef7010834d98ee7b"],"salt":"8a602792b24541b5f68923899f7ef36049e776c7b10b3c37fa522d2c39850677","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":"2","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":"8cfb212400e48962cc9bb94aa661245796414c71fd045c38f3475886a87e7729","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":null},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"c21ecbffa27f0c8bf191283baed5abe5d7db541ab9259106470ac34563ae1d23","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"dc1807d1a3abbd969f855a838309443c2ce8123a2dbed8843323a8eb420accf7","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"_Q_GAdIvmjcJ1clVw_2g0POX98nLGWTqZZ-crdHzZs0weRwacWUcmHWoATt3nPgPO1HzplY_7W1DorXS3mPXBg"},"schema":"pubphys.envelope/1"},"record_hash":"c21ecbffa27f0c8bf191283baed5abe5d7db541ab9259106470ac34563ae1d23","leaf_index":3668}