On Integrable Structures on Non-compact Boundaries in Three-Dimensional Gravity
arXiv:2607.06867
The paper analyzes three-dimensional Einstein gravity with a negative cosmological constant on non‑compact spatial boundaries, deriving a radial flow for the quasi‑local stress tensor that implements a finite‑cutoff holographic T\bar T deformation and linking the boundary dynamics to integrable bi‑Hamiltonian hierarchies via inverse scattering.
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 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.
26 pages. This version includes additional references and minor improvements to the outlook section