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Ricci flow from the renormalization of nonlinear sigma models in the framework of Euclidean algebraic quantum field theory. (English) Zbl 1433.81115

Summary: 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 provide a mathematically rigorous proof that, at first order in perturbation theory, the renormalization group flow of the nonlinear Sigma model is the Ricci flow.

MSC:

81T10 Model quantum field theories
81T15 Perturbative methods of renormalization applied to problems in quantum field theory
81T17 Renormalization group methods applied to problems in quantum field theory
81R20 Covariant wave equations in quantum theory, relativistic quantum mechanics
81R15 Operator algebra methods applied to problems in quantum theory
81T08 Constructive quantum field theory
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