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arXiv · 2510.10519

Integrability in Three-Dimensional Gravity: Eigenfunction-Forced KdV Flows

Hamed Adami·Anouchah Latifi
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Abstract

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.

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Hamed Adami, Anouchah Latifi. 2026-04-13. Integrability in Three-Dimensional Gravity: Eigenfunction-Forced KdV Flows. https://arxiv.org/abs/2510.10519

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