The DSSYK model emerges as the dynamics on the quantum homogeneous space of the von Neumann algebraic quantum group SU_q(1,1) ⋊ Z2.
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Verlinde,Double-scaled SYK, chords and de Sitter gravity,JHEP03(2025) 076 [2402.00635]
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Pairs of large-N 1D CFTs encode generalized free fields on a timelike geodesic in de Sitter space via large-N factorization, 1D conformal symmetry, and split representations of dS Green functions.
Proposes an SL(2,Z) sum of Kerr-lens geometries in 3d dS gravity whose spectral density is computed via crosscap amplitudes in CLS ⊗ CLS, matching semi-classical predictions and reducing in a simple case to GΣ ⊗ GΣ on the observer worldline.
The Euclidean path integral on elliptic de Sitter defines a no-boundary density matrix whose entropies reduce to vertex operator correlators on non-orientable surfaces, with a one-dimensional global Hilbert space but nontrivial observer Fock spaces.
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.
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.
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The von Neumann algebraic quantum group $\mathrm{SU}_q(1,1)\rtimes \mathbb{Z}_2$ and the DSSYK model
The DSSYK model emerges as the dynamics on the quantum homogeneous space of the von Neumann algebraic quantum group SU_q(1,1) ⋊ Z2.
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Generalized Free Fields in de Sitter from 1D CFT
Pairs of large-N 1D CFTs encode generalized free fields on a timelike geodesic in de Sitter space via large-N factorization, 1D conformal symmetry, and split representations of dS Green functions.
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An observer's quantization of 3d de Sitter
Proposes an SL(2,Z) sum of Kerr-lens geometries in 3d dS gravity whose spectral density is computed via crosscap amplitudes in CLS ⊗ CLS, matching semi-classical predictions and reducing in a simple case to GΣ ⊗ GΣ on the observer worldline.
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No boundary density matrix in elliptic de Sitter dS/$\mathbb{Z}_2$
The Euclidean path integral on elliptic de Sitter defines a no-boundary density matrix whose entropies reduce to vertex operator correlators on non-orientable surfaces, with a one-dimensional global Hilbert space but nontrivial observer Fock spaces.
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Cosmological Entanglement Entropy from the von Neumann Algebra of Double-Scaled SYK & Its Connection with Krylov Complexity
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.
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Probing the Chaos to Integrability Transition in Double-Scaled SYK
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.
- q-Askey Deformations of Double-Scaled SYK
- The Thermodynamics of Cosmological Horizons and Their Holographic Description in de Sitter Space
- Deforming the Double-Scaled SYK & Reaching the Stretched Horizon From Finite Cutoff Holography