https://neckpinch.com/authors/mauro-carfora/New arXiv papers by Mauro Carfora, from Neckpinch Tue, 10 Nov 2026 04:10:28 GMT https://neckpinch.com/papers/1809.07652/arxiv:1809.07652Thu, 20 Sep 2018 00:00:00 GMTMauro Carfora, Claudio Dappiaggi, Nicolò Drago, Paolo Rinaldi — The perturbative approach to nonlinear Sigma models and the associated renormalization group flow are discussed within the framework of Euclidean algebraic quantum field theory and of the principle of general local covariance. In particular we show in an Euclidean setting how to define Wick ordered powers of the underlying quantum fields and we classify the freedom in such procedure by extending to this setting a recent construction of Khavkine, Melati and Moretti for vector valued free fields. As a by-product of such classification, we prove that, at first order in perturbation theory, the renormalization group flow of the nonlinear Sigma model is the Ricci flow.Ricci flowPhysics https://neckpinch.com/papers/1805.09773/arxiv:1805.09773Thu, 24 May 2018 00:00:00 GMTMauro Carfora, Christine Guenther — Let (𝓜,g) be a closed Riemannian manifold. The second order approximation to the perturbative renormalization group flow for the nonlinear sigma model (RG-2 flow) is given by : ∂/∂t g(t) = −2 Ric(t) − fracα2 Rm²(t), where g = Riemannian metric, Ric = Ricci curvature, Rm²ᵢⱼ:=RᵢᵣₘₖRⱼ^(rmk), and α≥ 0 is a parameter. The flow is invariant under diffeomorphisms, but not under scaling of the metric. We first develop a geometrically defined coupling constant α_g that leads to an equivalent, scale-invariant flow. We further find a modified Perelman entropy for the flow, and prove local existence of the resulting variational system. The crucial idea is to modify the flow by two diffeomorphisms, the first being the usual DeTurck diffeomorphism the second being strictly related to the geometrical characterization of the coupling constant α_g. We minimize the entropy functional so introduced to characterize a natural extension Λ[g] of the Perelman's λ(g)–functional, and show that Λ[g] is monotonic under the RG-2 flow. Although the modified Perelman entropy is monotonic, the RG-2 flow is not a gradient flow with respect this functional. We discuss this issue in detail, showing how to deform the functional in order to give rise to a gradient flow for a DeTurck modified RG-2 flow.Perelman entropyHarmonic maps & DeTurck trickPhysics