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Pluriclosed flow and the Hull-Strominger system

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arxiv 2408.11674 v1 pith:OTSQ4UMR submitted 2024-08-21 math.DG math.AP

Mario Garcia-Fernandez , Raul Gonzalez Molina , Jeffrey Streets This is my paper · ORCID
classification math.DGmath.AP
keywords flowhull-stromingersystemsolutionsalgebroidsestimateshigherpluriclosed
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abstract

We define a natural extension of pluriclosed flow aiming at constructing solutions of the Hull-Strominger system. We give several geometric formulations of this flow, which yield a series of a priori estimates for the flow and also for the Hull-Strominger system. The evolution equations are derived using the theory of string algebroids, a class of Courant algebroids which occur naturally in higher gauge theory. Using this, we interpret the flow as generalized Ricci flow and also as a higher/coupled version of Hermitian-Yang-Mills flow, proving furthermore that it is compatible with symmetry reduction. Regarding our main analytical results, we prove a priori $C^{\infty}$ estimates for uniformly parabolic solutions. This in particular settles the question of smooth regularity of uniformly elliptic solutions of the Hull-Strominger system, generalizing Yau's $C^3$ estimate for the complex Monge-Amp\`ere equation. We prove global existence and convergence results for the flow on special backgrounds, and discuss a conjectural relationship of the flow to the geometrization of Reid's fantasy.

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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. The canonical symmetry reduction of string backgrounds

    math.DG 2025-11 conditional novelty 6.0 of 10

    A compact string background with nonvanishing canonical symmetry reduces to a transverse string generalized Ricci soliton that is conformally co-closed, with explicit torsion in SU(3), G2, and Spin(7).

  2. Stringy Corrections to Heterotic SU(3)-Geometry

    hep-th 2025-07 accept novelty 6.0 of 10

    At second order in alpha', heterotic SU(3) compactifications with a smooth large-radius limit obey the same complex geometric equations as Strominger's first-order system, and the Hull connection is not an instanton.

  3. An introduction to conifold transitions

    math.DG 2025-08 conditional novelty 5.0 of 10

    Survey of conifold transitions between Calabi-Yau threefolds with a sketched differential-geometric proof of the necessity part of Friedman's smoothing criterion.

  4. Calabi-Yau threefolds across quadratic singularities

    math.DG 2025-01 unverdicted

    This paper is a survey of the geometry of conifold transitions between Calabi-Yau threefolds, focusing on non-Kähler outputs and the structures they carry.

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