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Peer-reviewedCC BY 4.0SciPost Physics

On integrable structures on non–compact boundaries in three–dimensional gravity

  • Hamed Adami1,2
  • Kristiansen Lara3,4
  • Anouchah Latifi5
  • René Meyer2,6,7
7 affiliations
  1. 1Fudan University
  2. 2Shanghai Institute for Mathematics and Interdisciplinary Sciences
  3. 3Center for Scientific Studies
  4. 4San Sebastián University
  5. 5Qom University of Technology
  6. 6University of Würzburg
  7. 7Würzburg-Dresden Cluster of Excellence
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Abstract

We study three-dimensional Einstein gravity with negative cosmological constant on non-compact spatial boundaries within the Chern-Simons formulation. Using an exact fluid/gravity correspondence, we derive a closed radial flow equation for the quasi-local stress tensor and show that it realizes the holographic \sqrt{T\bar T} T T ‾ deformation at finite cutoff. We further develop the inverse-scattering description of the boundary dynamics, identifying the gravitational interpretation of the associated spectral data and analyzing the finite-cutoff deformation of soliton solutions. Although the boundary evolution is governed by an integrable bi-Hamiltonian hierarchy, we show that the radial flow itself is not Hamiltonian with respect to the canonical Poisson structure. Our results establish a unified framework connecting integrability, quasi-local gravitational observables, inverse scattering, and finite-cutoff holography on non-compact boundaries.

Versions

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Cite

BibTeXRIS
BibTeX
@article{adami2026integrable,
  title = {{On integrable structures on non–compact boundaries in three–dimensional gravity}},
  author = {Hamed Adami and Kristiansen Lara and Anouchah Latifi and René Meyer},
  journal = {SciPost Physics},
  year = {2026},
  month = oct,
  doi = {10.21468/scipostphys.21.4.092},
  url = {https://scipost.org/10.21468/SciPostPhys.21.4.092},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - On integrable structures on non–compact boundaries in three–dimensional gravity
AU  - Hamed Adami
AU  - Kristiansen Lara
AU  - Anouchah Latifi
AU  - René Meyer
PY  - 2026
DA  - 2026/10/13
JO  - SciPost Physics
DO  - 10.21468/scipostphys.21.4.092
UR  - https://scipost.org/10.21468/SciPostPhys.21.4.092
AB  - We study three-dimensional Einstein gravity with negative cosmological constant on non-compact spatial boundaries within the Chern-Simons formulation. Using an exact fluid/gravity correspondence, we derive a closed radial flow equation for the quasi-local stress tensor and show that it realizes the holographic \sqrt{T\bar T} T T ‾ deformation at finite cutoff. We further develop the inverse-scattering description of the boundary dynamics, identifying the gravitational interpretation of the associated spectral data and analyzing the finite-cutoff deformation of soliton solutions. Although the boundary evolution is governed by an integrable bi-Hamiltonian hierarchy, we show that the radial flow itself is not Hamiltonian with respect to the canonical Poisson structure. Our results establish a unified framework connecting integrability, quasi-local gravitational observables, inverse scattering, and finite-cutoff holography on non-compact boundaries.
SN  - 2542-4653
ER  -