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PreprintCC BY 4.0arXiv

Integrability in Asymptotic Symmetries of Spacetime: the BMS3 scenario

  • Corentin Vitel
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Abstract

We discuss the existence of a well-defined bms3-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 bms3 bi-Hamiltonian structure is constructed on which a Nijenhuis operator can be attached. A similar argument is made for the AdS3 case, where we check that the flat limit of the latter recovers the asymptotically flat situation. An alternative τ-scheme description is also presented. Moreover, a Lie-Poisson description suggests that such a bms3-hierarchy is not unique. For a subclass of so-called energy-dependent Schrödinger operators, it is shown that their Lax flows are described by the coadjoint orbits of bms3.

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Cite

BibTeXRIS
BibTeX
@misc{vitel2026integrability,
  title = {{Integrability in Asymptotic Symmetries of Spacetime: the $\textBMS_3$ scenario}},
  author = {Corentin Vitel},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2607.28454},
  eprint = {2607.28454},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2607.28454},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Integrability in Asymptotic Symmetries of Spacetime: the BMS_3 scenario
AU  - Corentin Vitel
PY  - 2026
DA  - 2026/10/07
PB  - arXiv
DO  - 10.48550/arxiv.2607.28454
UR  - https://arxiv.org/abs/2607.28454
AB  - We discuss the existence of a well-defined 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 bms_3 bi-Hamiltonian structure is constructed on which a Nijenhuis operator can be attached. A similar argument is made for the AdS_3 case, where we check that the flat limit of the latter recovers the asymptotically flat situation. An alternative τ-scheme description is also presented. Moreover, a Lie-Poisson description suggests that such a bms_3-hierarchy is not unique. For a subclass of so-called energy-dependent Schrödinger operators, it is shown that their Lax flows are described by the coadjoint orbits of bms_3.
ER  -