Paper · Apr 30, 2021

Strings in Bimetric Spacetimes

Ziqi Yan

hep-tharXiv:2105.00011v4
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As on arXiv

Abstract

We put forward a two-dimensional nonlinear sigma model that couples (bosonic) matter fields to topological Horava gravity on a nonrelativistic worldsheet. In the target space, this sigma model describes classical strings propagating in a curved spacetime background, whose geometry is described by two distinct metric fields. We evaluate the renormalization group flows of this sigma model on a flat worldsheet and derive a set of beta-functionals for the bimetric fields. Imposing worldsheet Weyl invariance at the quantum level, we uncover a set of gravitational field equations that dictate the dynamics of the bimetric fields in the target space, where a unique massless spin-two excitation emerges. When the bimetric fields become identical, the sigma model gains an emergent Lorentz symmetry. In this single metric limit, the beta-functionals of the bimetric fields reduce to the Ricci flow equation that arises in bosonic string theory, and the bimetric gravitational field equations give rise to Einstein's gravity.

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Submitted
Apr 30, 2021
Last revised
Oct 10, 2022 (v4)
Subjects
hep-th, gr-qc
Journal
JHEP 09 (2021) 164
DOI
10.1007/JHEP09(2021)164

Comments: 42 pages; v2: minor clarifications; v3: minor clarifications, typos fixed; v4: minor typos

Ricci flowSurfacesPhysics

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)6Andino 2018 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., 2018)4Carfora 2018 Cosmology from the two-dimensional renormalization group acting as the Ricci flow (Daniel Friedan, 2019)7Friedan 2019 Flag manifold sigma models: spin chains and integrable theories (Ian Affleck, Dmitri Bykov and Kyle Wamer, 2021)1Affleck 2021 Sigma models as Gross-Neveu models (Dmitri Bykov, 2021)8Bykov 2021 Monotonicity of RG flow in emergent dual holography of worldsheet nonlinear σ model (Ki-Seok Kim, Arpita Mitra, Debangshu Mukherjee et al., 2024)5Kim 2024 Scale and Conformal Invariance in 2d Sigma Models, with an Application to N=4 Supersymmetry (Georgios Papadopoulos and Edward Witten, 2024)2Papadopoulos 2024 Sigma model renormalisation group flows, singularities and some remarks on cosmology (Georgios Papadopoulos, 2025)3Papadopoulos 2025
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  1. Flag manifold sigma models: spin chains and integrable theories

    Ian Affleck, Dmitri Bykov and Kyle Wamer

    Topics Surfaces, Physics · Shared terms “sigma model”, “target space”, “renormalization group”

  2. Scale and Conformal Invariance in 2d Sigma Models, with an Application to N=4 Supersymmetry

    Georgios Papadopoulos and Edward Witten

    Topics Surfaces, Physics · Shared terms “sigma model”, “target space”, “invariance”

  3. Sigma model renormalisation group flows, singularities and some remarks on cosmology

    Georgios Papadopoulos

    Topics Surfaces, Physics · Shared terms “sigma model”, “group flow”, “target space”

  4. 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 “sigma model”, “nonlinear Sigma”, “group flow”

  5. Monotonicity of RG flow in emergent dual holography of worldsheet nonlinear model

    Ki-Seok Kim, Arpita Mitra, Debangshu Mukherjee et al.

    Topics Physics · Shared terms “worldsheet”, “target space”, “emergent”

  6. RG-2 flow, mass and entropy

    Oscar Lasso Andino

    Topics Surfaces, Physics · Shared terms “sigma model”, “group flow”, “renormalization group”

  7. Cosmology from the two-dimensional renormalization group acting as the Ricci flow

    Daniel Friedan

    Topics Surfaces, Physics · Shared terms “gravitational field”, “renormalization group”, “describe”

  8. Sigma models as Gross-Neveu models

    Dmitri Bykov

    Topics Physics · Shared terms “sigma model”, “target space”

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) Surfaces On surfaces Ricci flow is conformal and scalar. It gives a heat-flow proof of the uniformization theorem: every closed surface converges to constant… Start with: The Ricci flow on surfaces (Hamilton, 1988) 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. 11A.12
    Ricci Flow on SurfacesBook 11A · The Ricci Flow: Existence and Maximum Principles

    Uniformization by Ricci flow, and Hamilton’s entropy.

  3. 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.