Paper · Oct 22, 2026

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

G. Bonelli, S. Lacroix, T. Pedroni, A. Tanzini

hep-tharXiv:2610.31672
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As on arXiv

Abstract

We construct a family of integrable 2d sigma models through 4d Chern-Simons theory and show that their classical point-particle reduction corresponds to a Hitchin system. The integrable Hitchin quantisation then provides a natural candidate Hamiltonian for the one-loop reduced dynamics of the sigma models, which coincides with the Perelman operator in all cases examined. This allows us to study the corresponding spectral problems using 4d gauge theory and 2d conformal field theory methods. For the sausage model, we derive exact quantisation conditions and compute exponentially small corrections essential for the agreement with numerical finite-volume results.

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Submitted
Oct 22, 2026
Subjects
hep-th, math-ph

Comments: 7+5 pages, 1 figure

Ricci flow4-manifoldsEigenvalues & spectrumPhysicsNumerics & visualization

Its neighbourhood

Connected papers

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 2021, 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 Integrability and RG flow in 2d sigma models (Nat Levine, 2021)2Levine 2021 Spinors and mass on weighted manifolds (Julius Baldauf and Tristan Ozuch, 2022)8Baldauf 2022 Harmonic spinors in the Ricci flow (Julius Baldauf, 2022)5Baldauf 2022 Nonassociative geometric and quantum information flows and R-flux deformations of wormhole solutions in string gravity (Laurenţiu Bubuianu, Douglas Singleton, Sergiu I. Vacaru et al., 2024)6Bubuianu 2024 Scale and Conformal Invariance in 2d Sigma Models, with an Application to N=4 Supersymmetry (Georgios Papadopoulos and Edward Witten, 2024)3Papadopoulos 2024 On dual regime in Yang-Baxter deformed O(2N) sigma models (Alexey Bychkov and Alexey Litvinov, 2025)1Bychkov 2025 Conformal-Mapping Method for Horizon Multipoles in Numerical Relativity: Implementation, Kerr Validation, and Applications Beyond Axisymmetry (Yeong-Bok Bae, Young-Hwan Hyun and Gungwon Kang, 2026)4Bae 2026 Using Ricci Flow in the Construction of Homogeneous Cosmological Models (Fan Zhang and Lee Lindblom, 2026)7Zhang 2026
Closer to the centre: more closely connected. Clockwise from the top: oldest to newest. Ricci flowWider flowsalso connected to each other
  1. On dual regime in Yang-Baxter deformed sigma models

    Alexey Bychkov and Alexey Litvinov

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

  2. Integrability and RG flow in 2d sigma models

    Nat Levine

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

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

    Georgios Papadopoulos and Edward Witten

    Topics Physics · Shared terms “sigma model”, “field theory”

  4. Conformal-Mapping Method for Horizon Multipoles in Numerical Relativity: Implementation, Kerr Validation, and Applications Beyond Axisymmetry

    Yeong-Bok Bae, Young-Hwan Hyun and Gungwon Kang

    Topics Numerics & visualization, Eigenvalues & spectrum, Physics · Shared terms “numerical”, “spectral”

  5. Harmonic spinors in the Ricci flow

    Julius Baldauf

    Topics 4-manifolds · Shared terms “Seiberg Witten”, “Hitchin”, “Perelman”

  6. Nonassociative geometric and quantum information flows and R-flux deformations of wormhole solutions in string gravity

    Laurenţiu Bubuianu, Douglas Singleton, Sergiu I. Vacaru et al.

    Topics 4-manifolds, Physics · Shared terms “Perelman”

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

    Fan Zhang and Lee Lindblom

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

  8. Spinors and mass on weighted manifolds

    Julius Baldauf and Tristan Ozuch

    Topics Eigenvalues & spectrum, Physics · Shared terms “Witten”, “spectral”, “Perelman”

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) 4-manifolds Four is the first dimension where Ricci flow's singularities are not fully understood. It is also the dimension of the smooth Poincaré conjecture… Start with: The topology of four-dimensional manifolds (Freedman, 1982) Eigenvalues & spectrum Perelman's λ-functional is the lowest eigenvalue of −4Δ+ R, and it never decreases along Ricci flow. Start with: The entropy formula for the Ricci flow and its geometric applications (Perelman, 2002) 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. 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. 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.

  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.