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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The Spectrum in the Sachdev-Ye-Kitaev Model
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abstract
The SYK model consists of $N\gg 1$ fermions in $0+1$ dimensions with a random, all-to-all quartic interaction. Recently, Kitaev has found that the SYK model is maximally chaotic and has proposed it as a model of holography. We solve the Schwinger-Dyson equation and compute the spectrum of two-particle states in SYK, finding both a continuous and discrete tower. The four-point function is expressed as a sum over the spectrum. The sum over the discrete tower is evaluated.
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Derives the all-order fluctuating hydrodynamics effective action and transport coefficients for the SYK lattice from its microscopic pseudo-Goldstone boson action.
Projective geometry and Cayley transformations provide a common framework for the free particle-oscillator correspondences via the Schwarzian cocycle.
Fractional operator powers generate non-positivity constraints that determine the SYK bilinear spectrum and converge to exact eigenvalues under truncation.
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.
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.
At large central charge, BCFT von Neumann entropy with deformed boundaries is reproduced by island entropy in an emergent JT gravity setup with transparent boundary conditions set by the deformation.
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.
Lecture notes introducing the 1/N expansion and melonic limit of tensor models, which yield new conformal field theories.
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.
citing papers explorer
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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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All-order fluctuating hydrodynamics of the SYK lattice
Derives the all-order fluctuating hydrodynamics effective action and transport coefficients for the SYK lattice from its microscopic pseudo-Goldstone boson action.
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Projective Time, Cayley Transformations and the Schwarzian Geometry of the Free Particle--Oscillator Correspondence
Projective geometry and Cayley transformations provide a common framework for the free particle-oscillator correspondences via the Schwarzian cocycle.
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Quantum mechanical bootstrap without inequalities: SYK bilinear spectrum
Fractional operator powers generate non-positivity constraints that determine the SYK bilinear spectrum and converge to exact eigenvalues under truncation.
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Emergent States and Algebras from the Double-Scaling limit of Pure States in SYK
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.
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Single-Sided Black Holes in Double-Scaled SYK Model and No Man's Island
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.
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Large-c BCFT Entanglement Entropy with Deformed Boundaries from Emergent JT Gravity
At large central charge, BCFT von Neumann entropy with deformed boundaries is reproduced by island entropy in an emergent JT gravity setup with transparent boundary conditions set by the deformation.
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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.
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Notes on Tensor Models and Tensor Field Theories
Lecture notes introducing the 1/N expansion and melonic limit of tensor models, which yield new conformal field theories.
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Quantum chaos and the holographic principle
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.