Functional renormalization group flow is recast as a potential-modified Ricci flow on the Fisher information metric of coupling space, with an RG-flow entropy serving as the infinite-dimensional analog of Perelman's F-entropy and fixed points appearing as Ricci solitons.
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Functional Renormalization Group as a Ricci Flow: An \(\mathcal{F}\)-Entropy Perspective on Information Metric Dynamics
Functional renormalization group flow is recast as a potential-modified Ricci flow on the Fisher information metric of coupling space, with an RG-flow entropy serving as the infinite-dimensional analog of Perelman's F-entropy and fixed points appearing as Ricci solitons.