Paper · Jul 10, 2019

Integrable 2d sigma models: quantum corrections to geometry from RG flow

Ben Hoare, Nat Levine, Arkady A. Tseytlin

hep-tharXiv:1907.04737v2
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Abstract

Classically integrable -models are known to be solutions of the 1-loop RG equations, or "Ricci flow", with only a few couplings running. In some of the simplest examples of integrable deformations we find that in order to preserve this property at 2 (and higher) loops the classical -model should be corrected by quantum counterterms. The pattern is similar to that of effective -models associated to gauged WZW theories. We consider in detail the examples of the -deformation of ("sausage model") and , as well as the closely related -deformation of the coset. We also point out that similar counterterms are required in order for non-abelian duality to commute with RG flow beyond the 1-loop order.

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Submitted
Jul 10, 2019
Last revised
Oct 31, 2019 (v2)
Subjects
hep-th
DOI
10.1016/j.nuclphysb.2019.114798

Comments: 17 pages; v2: minor corrections

Ricci flowPhysics

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  3. Ricci flow of Integrable Sigma Models, Hitchin Systems and Quantum Seiberg-Witten theory

    G. Bonelli, S. Lacroix, T. Pedroni et al.

    Topics Physics · Shared terms “sigma model”, “integrable”, “sausage model”

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  5. On dual regime in Yang-Baxter deformed sigma models

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    Topics Physics · Shared terms “sigma model”, “integrable”

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

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    Topics Physics · Shared terms “sigma model”

  7. Flag manifold sigma models: spin chains and integrable theories

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  8. Sigma models as Gross-Neveu models

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    Topics Physics · Shared terms “sigma model”, “integrable”

Read around it

Background reading

The guides for the topics of this paper: what each idea is, why it matters, and the papers to read first.

Ricci flow Hamilton's Ricci flow evolves a Riemannian metric by minus twice its Ricci curvature. It is a nonlinear heat equation for geometry: it spreads… Start with: Three-manifolds with positive Ricci curvature (Hamilton, 1982) Physics Ricci flow first appeared in physics, as the leading-order renormalization-group flow of the string sigma model (Friedan, 1980). Start with: Nonlinear Models in 2+ε Dimensions (Friedan, 1980)

In the guidebook

  1. 5A.5
    Uniformization and the Two-Dimensional Ricci FlowBook 5A · Complex Analysis and Conformal Geometry

    Constant-curvature metrics on surfaces, and Ricci flow as a heat equation for the conformal factor.

  2. 10A.12
    Curve Shortening and Minimal DiscsBook 10A · Three-Manifolds and Geometrization

    How loops shrink under curvature, how the discs they bound lose area, and Perelman's extinction estimate.

  3. 11A.1
    The Equation and Its First SolutionsBook 11A · The Ricci Flow: Existence and Maximum Principles

    A heat equation for the metric: spheres, cylinders and scaling.