Integrability in Three-Dimensional Gravity: Eigenfunction-Forced KdV Flows
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866908956136308736 |
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| author | Adami, Hamed Latifi, Anouchah |
| author_facet | Adami, Hamed Latifi, Anouchah |
| contents | We uncover a direct connection between three-dimensional gravity with chiral boundary conditions and a class of forced integrable systems. Starting from the Chern-Simons formulation, we derive consistent boundary conditions on a non-compact spatial slice, leading to boundary dynamics described by the potential modified KdV hierarchy. The dynamics reduce to a forced KdV equation, where the forcing term is determined self-consistently by the eigenfunctions of the associated Schrödinger operator. Using the inverse scattering transform, the reflectionless sector is solved via the Gelfand-Levitan-Marchenko method, while the radiative sector exhibits universal dispersive decay. This framework unifies AdS$_3$ boundary dynamics with integrable hierarchies and elucidates the roles of solitons and radiation in the dual conformal field theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_10519 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Integrability in Three-Dimensional Gravity: Eigenfunction-Forced KdV Flows Adami, Hamed Latifi, Anouchah High Energy Physics - Theory General Relativity and Quantum Cosmology We uncover a direct connection between three-dimensional gravity with chiral boundary conditions and a class of forced integrable systems. Starting from the Chern-Simons formulation, we derive consistent boundary conditions on a non-compact spatial slice, leading to boundary dynamics described by the potential modified KdV hierarchy. The dynamics reduce to a forced KdV equation, where the forcing term is determined self-consistently by the eigenfunctions of the associated Schrödinger operator. Using the inverse scattering transform, the reflectionless sector is solved via the Gelfand-Levitan-Marchenko method, while the radiative sector exhibits universal dispersive decay. This framework unifies AdS$_3$ boundary dynamics with integrable hierarchies and elucidates the roles of solitons and radiation in the dual conformal field theory. |
| title | Integrability in Three-Dimensional Gravity: Eigenfunction-Forced KdV Flows |
| topic | High Energy Physics - Theory General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2510.10519 |