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## Geometric flows and supersymmetry

Anthony Ashmore
• Function : Author
Ruben Minasian
• Function : Author
Yann Proto
• Function : Author

#### Abstract

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 eight-manifolds 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 $\alpha'$ 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.

### Dates and versions

hal-04009997 , version 1 (01-03-2023)

### Identifiers

• HAL Id : hal-04009997 , version 1
• ARXIV :
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### Cite

Anthony Ashmore, Ruben Minasian, Yann Proto. Geometric flows and supersymmetry. 2023. ⟨hal-04009997⟩

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