Paper · Jul 20, 2020

The quantum non-linear -model RG flow and integrability in wormhole geometries

Oscar Lasso Andino, Christian L. Vásconez

gr-qcarXiv:2007.10422v3
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Abstract

The target space of the non-linear -model is a Riemannian manifold. Although it can be any Riemannian metric, there are certain physically interesting geometries which are worth to study. Here, we numerically evolve the time-symmetric foliations of a family of spherically symmetric asymptotically flat wormholes under the -loop renormalization group flow of the non-linear -model, the Ricci flow, and under the -loop approximation, RG-2 flow. We rely over some theorems adapted from the compact case for studying the evolution of different wormhole types, specially those with high curvature zones. Some metrics expand and others contract at the beginning of the flow, however, all metrics pinch-off at a certain time. This is related with the fact that the flow does not converge to a fixed point when its starting geometry is the spatial sections of a Morris-Thorne wormhole, and therefore the corresponding non-linear -model is non-integrable/renormalizable. We present a numerical study of the evolution of wormhole singularities in three dimensions extending the theoretical estimations. Finally, we compute the evolution of the Hamilton's entropy and the Brown-York energy.

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Submitted
Jul 20, 2020
Last revised
Feb 1, 2023 (v3)
Subjects
gr-qc, hep-th
Journal
Nuclear Physics B, Volume 990, 2023, 116178
DOI
10.1016/j.nuclphysb.2023.116178

Comments: 18 pg

Ricci flowSingularitiesBoundaries & non-compactRotational symmetry & warped productsPhysicsNumerics & visualization

Its neighbourhood

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The 8 papers on this site closest to this one, judged by the topics they share, the words and phrases in their titles and abstracts, and their authors. They are not its citations, but a map of the work around it. Papers here go back to 2016, plus the canon.

Connected papers This paper in the centre and the 8 papers closest to it around it, in date order clockwise from the top. The closer a paper sits to the centre, the stronger the connection. This paper RG-2 flow, mass and entropy (Oscar Lasso Andino, 2018)1Andino 2018 A numerical stability analysis of mean curvature flow of noncompact hypersurfaces with Type-II curvature blowup (David Garfinkle, James Isenberg, Dan Knopf et al., 2021)7Garfinkle 2021 Integrability and RG flow in 2d sigma models (Nat Levine, 2021)6Levine 2021 Gradient flow of Einstein-Maxwell theory and Reissner-Nordström black holes (Davide De Biasio, Julian Freigang, Dieter Lust et al., 2022)2De Biasio 2022 Stability of piecewise flat Ricci flow (Rory Conboye, 2023)8Conboye 2023 Noise-induced stabilization of Schwarzschild–AdS black holes under stochastic Ricci flow (Jihui Wang, Matteo Lulli and Antonino Marciano, 2026)3Wang 2026 Using Ricci Flow in the Construction of Homogeneous Cosmological Models (Fan Zhang and Lee Lindblom, 2026)4Zhang 2026 Ricci flow of Integrable Sigma Models, Hitchin Systems and Quantum Seiberg-Witten theory (G. Bonelli, S. Lacroix, T. Pedroni et al., 2026)5Bonelli 2026
Closer to the centre: more closely connected. Clockwise from the top: oldest to newest. Ricci flowWider flowsalso connected to each other
  1. RG-2 flow, mass and entropy

    Oscar Lasso Andino

    Topics Physics, Boundaries & non-compact · Same author Oscar Lasso Andino · Shared terms “loop approximation”, “symmetric foliation”, “time symmetric”

  2. Gradient flow of Einstein-Maxwell theory and Reissner-Nordström black holes

    Davide De Biasio, Julian Freigang, Dieter Lust et al.

    Topics Numerics & visualization, Rotational symmetry & warped products, Physics · Shared terms “fixed point”, “spherically symmetric”, “numerically”

  3. Noise-induced stabilization of Schwarzschild–AdS black holes under stochastic Ricci flow

    Jihui Wang, Matteo Lulli and Antonino Marciano

    Topics Numerics & visualization, Rotational symmetry & warped products, Physics · Shared terms “spherically symmetric”, “fixed point”, “numerical”

  4. Using Ricci Flow in the Construction of Homogeneous Cosmological Models

    Fan Zhang and Lee Lindblom

    Topics Numerics & visualization, Physics · Shared terms “numerically”

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

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

    Topics Numerics & visualization, Physics · Shared terms “integrable”, “numerical”

  6. Integrability and RG flow in 2d sigma models

    Nat Levine

    Topics Physics · Shared terms “integrability”, “renormalizable”, “target space”

  7. A numerical stability analysis of mean curvature flow of noncompact hypersurfaces with Type-II curvature blowup

    David Garfinkle, James Isenberg, Dan Knopf et al.Wider flows

    Topics Numerics & visualization, Rotational symmetry & warped products, Boundaries & non-compact · Shared terms “numerical”

  8. Stability of piecewise flat Ricci flow

    Rory Conboye

    Topics Numerics & visualization · Shared terms “numerical”, “approximation”

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) Singularities On a closed manifold the flow can stop in finite time: curvature blows up, often because a neck pinches off. Start with: The formations of singularities in the Ricci Flow (Hamilton, 1993) Boundaries & non-compact Ricci flow beyond closed manifolds: complete non-compact spaces, manifolds with boundary, and asymptotically flat or hyperbolic ends. Start with: Deforming the metric on complete Riemannian manifolds (Shi, 1989) Rotational symmetry & warped products For rotationally symmetric metrics and warped products, Ricci flow reduces to a parabolic equation in one space variable. Start with: The ricci flow on radially symmetric R3 (Ivey, 1994)

In the guidebook

  1. 6D.11
    Computing Geometric FlowsBook 6D · Diffusions, Finance and Computation

    Numerical curve shortening and mean curvature flow, level sets and phase fields, discrete Ricci flow on surfaces and in conformal mapping, rotationally symmetric neckpinches, and what computation has taught about singularities.

  2. 11B.4
    Blow-Ups, Blow-Downs and Splitting at InfinityBook 11B · Solitons, Compactness and Singularities

    Limits of rescaled manifolds and flows: why blow-up limits are nonnegatively curved, what blow-downs see, and how lines appear at infinity.

  3. 11B.6
    Rotationally Symmetric Flows and the Standard SolutionBook 11B · Solitons, Compactness and Singularities

    The neckpinch in equations: warped products under the flow, what the maximum principle forces, and the standard solution that surgery glues in.