JT gravity in a box is quantized exactly by recasting its dynamics as Pöschl-Teller scattering, producing closed-form wavefunctions and correlators with finite-cutoff corrections beyond T Tbar.
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Solving the Schwarzian via the Conformal Bootstrap
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abstract
We obtain exact expressions for a general class of correlation functions in the 1D quantum mechanical model described by the Schwarzian action, that arises as the low energy limit of the SYK model. The answer takes the form of an integral of a momentum space amplitude obtained via a simple set of diagrammatic rules. The derivation relies on the precise equivalence between the 1D Schwarzian theory and a suitable large $c$ limit of 2D Virasoro CFT. The mapping from the 1D to the 2D theory is similar to the construction of kinematic space. We also compute the out-of-time ordered four point function. The momentum space amplitude in this case contains an extra factor in the form of a crossing kernel, or R-matrix, given by a 6j-symbol of SU(1,1). We argue that the R-matrix describes the gravitational scattering amplitude near the horizon of an AdS${}_2$ black hole. Finally, we discuss the generalization of some of our results to ${\cal N}=1$ and ${\cal N}=2$ supersymmetric Schwarzian QM.
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A semiclassical construction of fiducial observers in JT gravity, fixed by conformal isometry flow, is extended to the quantum regime to compute wormhole contributions yielding finite thermal entropy and a quantum description of the stretched horizon.
An SYK-based quantum system reproduces semiclassical correlators of quantum fields in rigid de Sitter space and non-trivial OTOC features including a doubled Lyapunov exponent.
Microscopic D-brane description of non-supersymmetric extremal black holes yields a unique ground state with non-zero energy, confirming absence of degeneracy.
A gapped parent Hamiltonian built from two copies of a target Hamiltonian plus ultra-local inter-copy couplings allows adiabatic preparation of high-fidelity thermofield double states for ETH-obeying systems.
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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Open-Channel Operator Closure of the Finite-Cutoff JT Gravity Disk Amplitude
The finite-cutoff JT gravity disk amplitude is reproduced via open-channel operators as a boundary-state matrix element, with the geodesic sector shown to be bandlimited and the branch-difference amplitude not equivalent to the thermal trace of any single lower-bounded β-independent Hamiltonian.