{"paper":{"title":"Functional Renormalization Group as a Ricci Flow: An $\\mathcal{F}$-Entropy Perspective on Information Metric Dynamics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Functional renormalization group flows are equivalent to Ricci flows on the information metric of coupling space.","cross_cats":[],"primary_cat":"hep-th","authors_text":"Ki-Seok Kim","submitted_at":"2026-05-17T01:16:38Z","abstract_excerpt":"We establish an equivalence between the Functional Renormalization Group (FRG) and the Ricci flow modified by a diffeomorphism. By reformulating the Polchinski exact renormalization group equation into an infinite-dimensional Fokker-Planck framework, we show that the evolution of the Fisher information metric on the coupling constant space is a geometric optimization process. Central to this mapping is our construction of a field-theoretic $\\mathcal{F}$-entropy functional - an infinite-dimensional analogue of Perelman's $\\mathcal{F}$-entropy functional - which acts as a Lyapunov potential for "},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We establish an equivalence between the Functional Renormalization Group (FRG) and the Ricci flow modified by a diffeomorphism. [...] the continuous scale evolution of the field distribution constitutes a Riemannian gradient flow of this F-entropy, which in turn deforms the information metric on the coupling constant space via the parametric Hessian of the entropic landscape. Crucially, the log of the effective action serves as a scalar potential Φ that generates the diffeomorphisms required to ensure the tensorial consistency of the flow.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The reformulation of the Polchinski exact renormalization group equation into an infinite-dimensional Fokker-Planck framework, together with the construction of the field-theoretic F-entropy functional as a Lyapunov potential whose gradient flow produces the claimed Ricci flow on the information metric (abstract, paragraphs describing the mapping and the role of Φ).","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"The functional renormalization group is equivalent to a diffeomorphism-modified Ricci flow on the information metric of coupling space, with the log effective action generating diffeomorphisms and an F-entropy serving as the driving Lyapunov functional toward a Ricci soliton.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Functional renormalization group flows are equivalent to Ricci flows on the information metric of coupling space.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"d2ccc14cb82adeacf485d620f8e069737d23b0b5c7903066dccbbd24f33815b3"},"source":{"id":"2605.17215","kind":"arxiv","version":1},"verdict":{"id":"d5f0eef2-18bf-4dad-8cfc-c6b83772f3f5","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T23:43:19.371918Z","strongest_claim":"We establish an equivalence between the Functional Renormalization Group (FRG) and the Ricci flow modified by a diffeomorphism. [...] the continuous scale evolution of the field distribution constitutes a Riemannian gradient flow of this F-entropy, which in turn deforms the information metric on the coupling constant space via the parametric Hessian of the entropic landscape. Crucially, the log of the effective action serves as a scalar potential Φ that generates the diffeomorphisms required to ensure the tensorial consistency of the flow.","one_line_summary":"The functional renormalization group is equivalent to a diffeomorphism-modified Ricci flow on the information metric of coupling space, with the log effective action generating diffeomorphisms and an F-entropy serving as the driving Lyapunov functional toward a Ricci soliton.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The reformulation of the Polchinski exact renormalization group equation into an infinite-dimensional Fokker-Planck framework, together with the construction of the field-theoretic F-entropy functional as a Lyapunov potential whose gradient flow produces the claimed Ricci flow on the information metric (abstract, paragraphs describing the mapping and the role of Φ).","pith_extraction_headline":"Functional renormalization group flows are equivalent to Ricci flows on the information metric of coupling space."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.17215/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"doi_title_agreement","ran_at":"2026-05-20T00:01:20.705292Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T23:52:41.642323Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-19T22:33:23.722169Z","status":"skipped","version":"1.0.0","findings_count":0},{"name":"claim_evidence","ran_at":"2026-05-19T22:01:57.925434Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"70bfaf6eb51b50388428b508ca8bdb9d609611af46493934b1fe7bff2dc20241"},"references":{"count":72,"sample":[{"doi":"","year":null,"title":"Probability Normalization and Dilaton-like Identification In Perelman’s theory of geometric evolution [21], the modified volume element under the conjugate heat equation framework is preserved via a d","work_id":"d5e0d50e-a737-4516-b876-c94179b4b923","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"Differentiating the ensemble-averaged representation established in Eq","work_id":"db550a2e-bf72-42e4-a5b4-a98012edd98e","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"Mapping onto the Consistency Condition and Eq. 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