https://neckpinch.com/authors/ki-seok-kim/New arXiv papers by Ki-Seok Kim, from Neckpinch Tue, 03 Nov 2026 08:41:12 GMT https://neckpinch.com/papers/2605.17215/arxiv:2605.17215Sun, 17 May 2026 00:00:00 GMTJin Mo Bok, Ki-Seok Kim — We establish a geometric correspondence between the Functional Renormalization Group (FRG) and a Ricci flow modified by a potential-driven diffeomorphism. By rewriting the Polchinski exact RG equation as an infinite-dimensional Fokker–Planck equation for field-distribution functionals, we show how a probability flow driven by a "thermodynamic" free-energy functional induces the evolution of the Fisher information metric on the coupling-constant manifold. Using the continuous scale-dissipation rate of this free-energy functional, we construct an RG-flow entropy functional that provides an infinite-dimensional counterpart of Perelman's 𝓕-entropy. The parametric Hessian of this RG-flow entropy then encodes the scale deformation of the Fisher information metric, thereby linking the JKO–Wasserstein flow in field-configuration space to the geometry of the coupling-constant manifold. An emergent scalar information potential Φ encodes the potential-driven diffeomorphism component, restoring the tensorial form of the flow under reparametrizations of the coupling coordinates. In this representation, the successive integration of high-energy degrees of freedom effectively smooths out the curvature of the information manifold, so that RG fixed points are realized as steady Ricci soliton equilibria. These results connect quantum field theory, optimal transport, and Perelman's theory of geometric evolution, providing a geometric framework for characterizing the stability, universality, and topological structure of quantum field theories.Ricci flowRicci solitonsLimit spaces & RCDStability & uniquenessPhysics https://neckpinch.com/papers/2404.09122/arxiv:2404.09122Sun, 14 Apr 2024 00:00:00 GMTKi-Seok Kim, Arpita Mitra, Debangshu Mukherjee, Shinsei Ryu — Based on the renormalization group (RG) flow of worldsheet bosonic string theory, we construct an effective holographic dual description of the target space theory identifying the RG scale with the emergent extra dimension. This results in an effective dilaton-gravity-gauge theory, analogous to the low-energy description of bosonic M-theory. We argue that this holographic dual effective field theory is non-perturbative in the α' expansion, where a class of string quantum fluctuations are resummed to all orders. To investigate the monotonicity of the RG flow of the target space metric in the emergent spacetime, we consider entropy production along the RG flow. We construct a microscopic entropy functional based on the probability distribution function of the holographic dual effective field theory, regarded as Gibbs- or Shannon-type entropy. Given that the Ricci flow represents the 1-loop RG flow equation of the target space metric for the 2D non-linear sigma model, and motivated by Perelman's proof of the monotonicity of Ricci flow, we propose a Perelman's entropy functional for the holographic dual effective field theory. This entropy functional is also non-perturbative in the α' expansion, and thus, generalizes the 1-loop result to the all-loop order. Furthermore, utilizing the equivalence between the Hamilton-Jacobi equation and the local RG equation, we suggest that the RG flow of holographic Perelman's entropy functional is the Weyl anomaly. This eventually reaffirms the monotonicity of RG flow for the emergent target spacetime but in a non-perturbative way. Interestingly, we find that the microscopic entropy production rate can be determined by integrating the rate of change of the holographic Perelman's entropy functional over all possible metric configurations along the flow.Ricci flowPerelman entropyPhysics