Paper · Nov 25, 2025

The canonical symmetry reduction of string backgrounds

Aaron Kennon, Jeffrey Streets

math.DGarXiv:2511.20773v2
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Abstract

String backgrounds, defined here as metric connections with skew-symmetric torsion and reduced holonomy, yield generalized Ricci solitons relative to the Lee vector field. By a variational argument using the string action, they are also gradient generalized Ricci solitons relative to a potential function. These two observations combine to yield a canonical symmetry, and in this work we derive fundamental features of the transverse geometry, and rigidity phenomena. We prove in a unified conceptual fashion that the transverse geometry satisfies the string generalized Ricci soliton equations (a simplified Hull-Strominger system) in many settings including almost Hermitian, almost contact, , , and geometry. We also show that the transverse geometry is always conformally co-closed, with the conformal factor given by the associated soliton potential.

Generalized & G₂ flowsRicci solitonsStability & uniquenessSasakian & contact geometry

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 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 Four-dimensional generalized Ricci flows with nilpotent symmetry (Steven Gindi and Jeffrey Streets, 2021)6Gindi 2021 Geometric Flows of G₂-Structures on 3-Sasakian 7-Manifolds (Aaron Kennon and Jason D. Lotay, 2022)4Kennon 2022 Generalized Ricci solitons and Einstein metrics on weak K-contact manifolds (Vladimir Rovenski, 2023)8Rovenski 2023 Optimal Transport and Generalized Ricci Flow (Eva Kopfer and Jeffrey Streets, 2023)5Kopfer 2023 Kähler Gradient Ricci Solitons with Large Symmetry (Hung Tran, 2023)7Tran 2023 Pluriclosed flow and the Hull-Strominger system (Mario Garcia-Fernandez, Raul Gonzalez Molina and Jeffrey Streets, 2024)1Garcia-Ferna 2024 Sasaki with torsion manifolds and string backgrounds (Beatrice Brienza, Anna Fino, Udhav Fowdar et al., 2026)3Brienza 2026 Topology of low-dimensional generalized Ricci solitons and string backgrounds (Jeffrey Streets, 2026)2Streets 2026
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  1. Pluriclosed flow and the Hull-Strominger system

    Mario Garcia-Fernandez, Raul Gonzalez Molina and Jeffrey Streets PDF

    Topics Generalized & G₂ flows · Same author Jeffrey Streets · Shared terms “Hull Strominger”, “Strominger system”, “symmetry reduction”

  2. Topology of low-dimensional generalized Ricci solitons and string backgrounds

    Jeffrey Streets PDF

    Topics Generalized & G₂ flows, Ricci solitons · Same author Jeffrey Streets · Shared terms “string backgrounds”, “holonomy”, “Hermitian”

  3. Sasaki with torsion manifolds and string backgrounds

    Beatrice Brienza, Anna Fino, Udhav Fowdar et al. PDF

    Topics Sasakian & contact geometry, Generalized & G₂ flows · Shared terms “string backgrounds”, “almost contact”, “Hermitian”

  4. Geometric Flows of -Structures on 3-Sasakian 7-Manifolds

    Aaron Kennon and Jason D. Lotay PDF

    Topics Sasakian & contact geometry, Generalized & G₂ flows, Stability & uniqueness · Same author Aaron Kennon

  5. Optimal Transport and Generalized Ricci Flow

    Eva Kopfer and Jeffrey Streets PDF

    Topics Generalized & G₂ flows · Same author Jeffrey Streets

  6. Four-dimensional generalized Ricci flows with nilpotent symmetry

    Steven Gindi and Jeffrey Streets PDF

    Topics Generalized & G₂ flows · Same author Jeffrey Streets

  7. Kähler Gradient Ricci Solitons with Large Symmetry

    Hung Tran PDF

    Topics Sasakian & contact geometry, Stability & uniqueness, Ricci solitons · Shared terms “almost Hermitian”, “almost contact”

  8. Generalized Ricci solitons and Einstein metrics on weak -contact manifolds

    Vladimir Rovenski PDF

    Topics Sasakian & contact geometry, Generalized & G₂ flows, Ricci solitons · Shared terms “vector field”

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.

Generalized & G₂ flows Ricci-type flows for geometry beyond Kähler metrics. Generalized Ricci flow couples a metric to a closed 3-form, pluriclosed and Chern–Ricci flows… Start with: A parabolic flow of pluriclosed metrics (Streets et al., 2009) Ricci solitons Metrics that change under Ricci flow only by scaling and diffeomorphisms: shrinking, steady or expanding solitons. Start with: The Ricci flow on surfaces (Hamilton, 1988) Stability & uniqueness When does a flow started near a special solution stay near it, and when is a flow determined by its data? Start with: Uniqueness of the Ricci Flow on Complete Noncompact Manifolds (Chen et al., 2005) Sasakian & contact geometry Sasakian manifolds are odd-dimensional manifolds whose metric cone is Kähler. They carry a transverse Kähler structure, so Kähler–Ricci flow has an… Start with: THE SASAKI–RICCI FLOW (SMOCZYK et al., 2010)

In the guidebook

  1. 11B.1
    Ricci SolitonsBook 11B · Solitons, Compactness and Singularities

    Self-similar solutions: the Gaussian, cylinders, the cigar and the Bryant soliton.

  2. 12B.2
    The Asymptotic Soliton and Three-Dimensional ShrinkersBook 12B · κ-Solutions and Surgery

    Perelman's Proposition 11.2 proved with Morgan and Tian: the reduced-length bounds on κ-solutions, the limit of rescalings, the equality case, and the classification of shrinking solitons in dimensions two and three.