Spinor flows with flux, I: short-time existence and smoothing estimates

Collins, Tristan C.; Phong, Duong H.

doi:10.48550/arxiv.2112.00814

Cited by 2 publications

(2 citation statements)

References 28 publications

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“…The flow has short-time existence with fixed points that are covariantly constant spinors. The case with flux was examined in [82], where a flow was introduced whose fixed points are spinors that are constant with respect to a covariant derivative but now with flux contributions. In addition, the flow for the flux enforces both its equation of motion and a Bianchi identity.…”

Section: Connections With Spinor Flowsmentioning

confidence: 99%

Geometric flows and supersymmetry

Ashmore¹,

Minasian²,

Proto³

2023

Preprint

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We study the relation between supersymmetry and geometric flows driven by the Bianchi identity for the three-form flux H in heterotic supergravity. We describe how the flow equations can be derived from a functional that appears in a rewriting of the bosonic action in terms of squares of supersymmetry operators.On a complex threefold, the resulting equations match what is known in the mathematics literature as "anomaly flow". We generalise this to seven-and eightmanifolds with G 2 or Spin(7) structures and discuss examples where the manifold is a torus fibration over a K3 surface. In the latter cases, the flow simplifies to a single scalar equation, with the existence of the supergravity solution implied by the long-time existence and convergence of the flow. We also comment on the α ′ expansion and highlight the importance of using the proper connection in the Bianchi identity to ensure that the flow's fixed points satisfy the supergravity equations of motion.

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Section: Connections With Spinor Flowsmentioning

confidence: 99%

Geometric flows and supersymmetry

Ashmore¹,

Minasian²,

Proto³

2023

Preprint

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“…Furthermore, the weighted variational formulas derived here generalize those from the unweighted case, which have recently received much attention: the gradient flow of the (unweighted) Dirichlet energy for spinors, introduced by Ammann-Weiss-Witt [AWW], is equivalent to a modified Ricci flow coupled to a spinor evolving parabolically in time [HW] (see also [AWW2,S,CP]). Additionally, the weighted variational formulas derived here are valid on all manifolds with boundary, so the techniques developed here are expected to extend to other geometries adapted to spin methods, such as asymptotically hyperbolic manifolds [Wa] and ALF manifolds [M].…”

Section: Introductionmentioning

confidence: 99%

The spinorial energy for asymptotically Euclidean Ricci flow

Baldauf¹,

Ozuch²

2022

Preprint

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This paper introduces a functional generalizing Perelman's weighted Hilbert-Einstein action and the Dirichlet energy for spinors. It is well-defined on a wide class of non-compact manifolds; on asymptotically Euclidean manifolds, the functional is shown to admit a unique critical point, which is necessarily of min-max type, and Ricci flow is its gradient flow. The proof is based on variational formulas for weighted spinorial functionals, valid on all spin manifolds with boundary.

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Spinor flows with flux, I: short-time existence and smoothing estimates

Cited by 2 publications

References 28 publications

Geometric flows and supersymmetry

Geometric flows and supersymmetry

The spinorial energy for asymptotically Euclidean Ricci flow

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