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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Chord diagrams, exact correlators in spin glasses and black hole bulk reconstruction
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abstract
The exact 2-point function of certain physically motivated operators in SYK-like spin glass models is computed, bypassing the Schwinger-Dyson equations. The models possess an IR low energy conformal window, but our results are exact at all time scales. The main tool developed is a new approach to the combinatorics of chord diagrams, allowing to rewrite the spin glass system using an auxiliary Hilbert space, and Hamiltonian, built on the space of open chord diagrams. We argue the latter can be interpreted as the bulk description and that it reduces to the Schwarzian action in the low energy limit.
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The DSSYK model emerges as the dynamics on the quantum homogeneous space of the von Neumann algebraic quantum group SU_q(1,1) ⋊ Z2.
q-Askey deformations of DSSYK produce transfer matrices from basic orthogonal polynomials whose chord numbers map to ER bridge lengths and signal geometric transitions with discrete spectra in sine dilaton gravity.
The supersymmetric index in a one-fermion matrix model for N=4 SYM is independent of N due to exact cancellations between bosonic and fermionic trace relations.
Berry curvature of BPS states is random-matrix-like for supersymmetric black hole microstates but non-random and often zero for horizonless geometries, offering a chaos diagnostic in degenerate sectors.
In double-scaled SYK, state-adapted dressed chord operators change the emergent algebra from Type II1 to Type I∞ and restore purity of KM states, unlike generic operators.
Wigner negativity in Krylov space stays O(1) or grows as t^{1/2} (without Hilbert-space scaling) in 2d CFTs, one-cut matrix models, and double-scaled SYK, indicating emergent semiclassicality.
Five-loop perturbative computation of DSSYK Krylov complexity equaling wormhole length in sine-dilaton gravity, with cumulants and all-order large-time resummation.
A general construction of contact interactions from chord diagrams is developed to match AdS2 scalar contact Witten diagrams in the SYK model.
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.
Algebraic entanglement entropy from type II1 algebras in double-scaled SYK is matched via triple-scaling limits to Ryu-Takayanagi areas in (A)dS2, reproducing Bekenstein-Hawking and Gibbons-Hawking formulas for specific regions while depending on Krylov complexity of the Hartle-Hawking state.
In the double-scaled SYK model with an end-of-the-world brane, the boundary algebra for a single-sided black hole is a type II1 von Neumann factor with non-trivial commutant, preventing full bulk reconstruction and creating a no man's island behind the horizon.
Establishes a threefold duality linking Krylov complexity growth rate to wormhole velocity and proper momentum in DSSYK holography, with higher moments capturing replica wormholes and Krylov entropy equaling parent-geometry von Neumann entropy after tracing baby universes.
A saddle point in the coupled SYK model yields a bulk geometry with a baby universe whose chord-diagram Hilbert space state is entangled with the exterior, giving evidence that closed universes can carry nontrivial quantum information.
The soft mode of DSSYK is dual to 3D near-de Sitter gravity with a localized dS2 slice, where effective actions, entropies, and correlators match via conformal boundary conditions on future and past infinity.
In SdS black hole holography, CV and CV2.0 complexities grow linearly while CA growth vanishes due to finite action, with matching rates between static patch and dS/CFT schemes.
A first-order phase transition in the Berkooz-Brukner-Jia-Mamroud interpolating model causes chord number, Krylov complexity, and operator size to switch discontinuously from chaotic (linear/exponential) to quasi-integrable (quadratic) growth.
Numerical study of the SYK-q spin model finds rapid entanglement growth to Haar-random saturation, a universal Rényi-1/2 mutual information vs negativity relation at minimal q, and Page-curve behavior in negativity under unequal partitions.
Krylov complexity is a canonical, parameter-independent measure of operator spreading that probes chaotic dynamics to late times and admits a geometric interpretation in holographic duals.
A review of the chaos-assisted holographic correspondence linking the SYK model to 2D JT gravity, including the need for string theory corrections at fine quantum scales.