Paper · Oct 27, 2016

Ricci flow, Courant algebroids, and renormalization of Poisson–Lie T-duality

Pavol Ševera, Fridrich Valach

math.DGarXiv:1610.09004
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As on arXiv

Abstract

We use a generalized Ricci tensor, defined for generalized metrics in Courant algebroids, to show that Poisson-Lie T-duality is compatible with the 1-loop renormalization group.

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Submitted
Oct 27, 2016
Subjects
math.DG, hep-th
DOI
10.1007/s11005-017-0968-5

Comments: 10 pages

Ricci flowPhysics

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  1. Ricci flow on Courant algebroids

    Jeffrey Streets, Charles Strickland-Constable and Fridrich Valach

    Topics Physics · Same author Fridrich Valach · Shared terms “Courant algebroids”, “generalized Ricci”

  2. Courant Algebroid Relations, T-Dualities and Generalised Ricci Flow

    Thomas C. De Fraja, Vincenzo Emilio Marotta and Richard J. Szabo

    Topics Ricci flow · Shared terms “Courant algebroids”, “compatible”, “Ricci tensor”

  3. Ricci flow, Killing spinors, and T-duality in generalized geometry

    Mario Garcia-Fernandez

    Topics Physics · Shared terms “Courant”, “algebroids”

  4. Generalized Ricci flow on nilpotent Lie groups

    Fabio Paradiso

    Topics Ricci flow · Shared terms “Courant algebroids”, “generalized Ricci”, “Lie”

  5. Classical and quantum integrable sigma models. Ricci flow, "nice duality" and perturbed rational conformal field theories

    Vladimir Fateev

    Topics Physics · Shared terms “renormalization”

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

    Mauro Carfora, Claudio Dappiaggi, Nicolò Drago et al.

    Topics Physics · Shared terms “renormalization”

  7. The perturbative Ricci flow in gravity

    Robert V. Harlander, Yannick Kluth, Jonas T. Kohnen et al.

    Topics Physics · Shared terms “renormalization”

  8. The homogeneous generalized Ricci flow

    Elia Fusi, Ramiro A. Lafuente and James Stanfield

    Topics Ricci flow · Shared terms “Courant algebroids”, “generalized Ricci”, “generalized metrics”

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.