Seminar talk, 22 May 2024

From Geometry of Differential Equations
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Speaker: Maxim Grigoriev

Title: Gauge PDEs on manifolds with boundaries and asymptotic symmetries

We propose a framework to study local gauge theories on manifolds with boundaries and their asymptotic symmetries, which is based on representing them as so-called gauge PDEs. These objects extend the conventional BV-AKSZ sigma-models to the case of not necessarily topological and diffeomorphism invariant systems and are known to behave well when restricted to submanifolds and boundaries. We introduce the notion of gauge PDE with boundaries, which takes into account generic boundary conditions, and apply the framework to asymptotically flat gravity. In so doing, we start with a suitable representation of gravity as a gauge PDE with boundaries, which implements the Penrose description of asymptotically simple spacetimes. We then derive the minimal model of the gauge PDE induced on the boundary and observe that it provides the Cartan (frame-like) description of a (curved) conformal Carollian structure on the boundary. Furthermore, imposing a version of the familiar boundary conditions in the induced boundary gauge PDE, leads immediately to the conventional BMS algebra of asymptotic symmetries.

Slides: Gauge_tractors_boundary.pdf

arXiv:2310.09637, arXiv:2212.11350; arXiv:1207.3439, arXiv:1305.0162, arXiv:1903.02820, arXiv:1009.0190