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The perturbative approach to nonlinear Sigma models and the associatedrenormalization group flow are discussed within the framework of Euclideanalgebraic quantum field theory and of the principle of general localcovariance. In particular we show in an Euclidean setting how to define Wickordered powers of the underlying quantum fields and we classify the freedom insuch procedure by extending to this setting a recent construction of Khavkine,Melati and Moretti for vector valued free fields. As a by-product of suchclassification, we prove that, at first order in perturbation theory, therenormalization group flow of the nonlinear Sigma model is the Ricci flow.

Ricci Flow from the Renormalization of Nonlinear Sigma Models in the Framework of Euclidean Algebraic Quantum Field Theory