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

Abstract

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.

arXiv comment24 pages

References in corpus (22)

• Ricci flow with surgery on three-manifolds
• The motion of point particles in curved spacetime
• The generally covariant locality principle -- A new paradigm for local quantum physics
• Microlocal Analysis and Interacting Quantum Field Theories: Renormalization on Physical Backgrounds
• Local Wick Polynomials and Time Ordered Products of Quantum Fields in Curved Spacetime
• Existence of Local Covariant Time Ordered Products of Quantum Fields in Curved Spacetime
• Conservation of the stress tensor in perturbative interacting quantum field theory in curved spacetimes
• On the Renormalization Group in Curved Spacetime
• Batalin-Vilkovisky formalism in perturbative algebraic quantum field theory
• Batalin-Vilkovisky formalism in the functional approach to classical field theory
• Local $\zeta$-function techniques vs point-splitting procedure: a few rigorous results
• One-loop stress-tensor renormalization in curved background: the relation between $\zeta$-function and point-splitting approaches, and an improved point-splitting procedure
• From euclidean field theory to quantum field theory
• The generalised principle of perturbative agreement and the thermal mass
• The effective theory of strings
• Analytic Dependence is an Unnecessary Requirement in Renormalization of Locally Covariant QFT
• Properties of field functionals and characterization of local functionals
• Locally covariant charged fields and background independence
• Euclidean Epstein-Glaser Renormalization
• Constructing Hadamard states via an extended Møller operator
• On Wick polynomials of boson fields in locally covariant algebraic QFT
• Extension of distributions, scalings and renormalization of QFT on Riemannian manifolds

Cited by in corpus (4)

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