Pith Number

pith:LQJGY6MB

pith:2026:LQJGY6MBVX2EVMBME5MCIH2V2C

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Functional Renormalization Group as a Ricci Flow: An $\mathcal{F}$-Entropy Perspective on Information Metric Dynamics

Ki-Seok Kim

Functional renormalization group flows are equivalent to Ricci flows on the information metric of coupling space.

arxiv:2605.17215 v1 · 2026-05-17 · hep-th

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Claims

C1strongest 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.

C2weakest 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).

C3one 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.

References

72 extracted · 72 resolved · 5 Pith anchors

[1] 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

[2] Differentiating the ensemble-averaged representation established in Eq

[3] Mapping onto the Consistency Condition and Eq. (A7) Taking the macroscopic expectation value of the microstate continuity equation under Fokker-Planck dynamics allows us to evaluate the right-hand sid

[4] Infinite-Dimensional Volume Invariance and Action Metric Identification Following Perelman’s theory of geometric evolution, the continuous modification of the path-integral measure must be compensated

[5] Functional Parametric Gradient and Hessian of Quantum Action To evaluate the twice-covariant derivative (the Hessian)∇ a∇bΦ governing the modified Ricci flow, we differentiate the functional definitio

Formal links

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Receipt and verification

First computed	2026-05-20T00:03:45.653966Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5c126c7981adf44ab02c2758241f55d0abf9b6bdbfb16c5cd4f0207ca6c33a2e

Aliases

arxiv: 2605.17215 · arxiv_version: 2605.17215v1 · doi: 10.48550/arxiv.2605.17215 · pith_short_12: LQJGY6MBVX2E · pith_short_16: LQJGY6MBVX2EVMBM · pith_short_8: LQJGY6MB

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curl -sH 'Accept: application/ld+json' https://pith.science/pith/LQJGY6MBVX2EVMBME5MCIH2V2C \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 5c126c7981adf44ab02c2758241f55d0abf9b6bdbfb16c5cd4f0207ca6c33a2e

Canonical record JSON

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    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "hep-th",
    "submitted_at": "2026-05-17T01:16:38Z",
    "title_canon_sha256": "f7022e4c73ba4520600e2b8357bda892f5f3ae5016ae5fd95922b5497b3803a2"
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