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arXiv · 2607.28454

Integrability in Asymptotic Symmetries of Spacetime: the $\text{BMS}_3$ scenario

Corentin Vitel
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Abstract

We revisit the proof of a $\mathfrak{bms}_3-$integrable hierarchy introduced in Fuentealba et al. (JHEP, 2018), using different structural methodologies. Specifically, from the variational complex on the ring of polynomial symbols, a $\mathfrak{bms}_3$ bi-Hamiltonian structure is constructed on which a Nijenhuis operator can be attached. A similar argument is made for the $\mathrm{AdS}_3$ case, where we check that the flat limit of the latter recovers the asymptotically flat situation. An alternative $\tau-$scheme description is also presented. Moreover, a Lie-Poisson description suggests that such a $\mathfrak{bms}_3-$hierarchy is not unique. For a subclass of so-called energy-dependent Schr\"odinger operators, it is shown that their Lax flows are described by the coadjoint orbits of $\mathfrak{bms}_3$.

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Corentin Vitel. 2026-07-30. Integrability in Asymptotic Symmetries of Spacetime: the $\text{BMS}_3$ scenario. https://arxiv.org/abs/2607.28454

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