Deformations of the double-scaled SYK model via finite-cutoff holography produce Krylov complexity as wormhole length and realize Susskind's stretched horizon proposal through targeted T² deformations in the high-energy spectrum.
The $\textrm{T}\bar{\textrm{T}}$ perturbation and its geometric interpretation
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abstract
Starting from the recently-discovered $\textrm{T}\bar{\textrm{T}}$-perturbed Lagrangians, we prove that the deformed solutions to the classical EoMs for bosonic field theories are equivalent to the unperturbed ones but for a specific field-dependent local change of coordinates. This surprising geometric outcome is fully consistent with the identification of $\textrm{T}\bar{\textrm{T}}$-deformed 2D quantum field theories as topological JT gravity coupled to generic matter fields. Although our conclusion is valid for generic interacting potentials, it first emerged from a detailed study of the sine-Gordon model and in particular from the fact that solitonic pseudo-spherical surfaces embedded in $\mathbb R^3$ are left invariant by the deformation. Analytic and numerical results concerning the perturbation of specific sine-Gordon soliton solutions are presented.
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Derives forced KdV equation from Chern-Simons 3D gravity with chiral boundaries, with forcing set by Schrödinger eigenfunctions, and solves reflectionless and radiative sectors via inverse scattering.
Finite cutoff in JT gravity causes faster ERB-length saturation, deformation-dependent baby-universe emission only under Lorentzian evolution, and possible one-cut universality corrections in the matrix dual.
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Integrability in Three-Dimensional Gravity: Eigenfunction-Forced KdV Flows
Derives forced KdV equation from Chern-Simons 3D gravity with chiral boundaries, with forcing set by Schrödinger eigenfunctions, and solves reflectionless and radiative sectors via inverse scattering.
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Finite cutoff JT gravity: Baby universes, Matrix dual, and (Krylov) Complexity
Finite cutoff in JT gravity causes faster ERB-length saturation, deformation-dependent baby-universe emission only under Lorentzian evolution, and possible one-cut universality corrections in the matrix dual.