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 World as a Hologram
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abstract
According to 't Hooft the combination of quantum mechanics and gravity requires the three dimensional world to be an image of data that can be stored on a two dimensional projection much like a holographic image. The two dimensional description only requires one discrete degree of freedom per Planck area and yet it is rich enough to describe all three dimensional phenomena. After outlining 't Hooft's proposal I give a preliminary informal description of how it may be implemented. One finds a basic requirement that particles must grow in size as their momenta are increased far above the Planck scale. The consequences for high energy particle collisions are described. The phenomena of particle growth with momentum was previously discussed in the context of string theory and was related to information spreading near black hole horizons. The considerations of this paper indicate that the effect is much more rapid at all but the earliest times. In fact the rate of spreading is found to saturate the bound from causality. Finally we consider string theory as a possible realization of 't Hooft's idea. The light front lattice string model of Klebanov and Susskind is reviewed and its similarities with the holographic theory are demonstrated. The agreement between the two requires unproven but plausible assumptions about the nonperturbative behavior of string theory. Very similar ideas to those in this paper have been long held by Charles Thorn.
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DSSYK∞ at infinite temperature duals in the flat-space limit to the 't Hooft model, and holographic entropy at TB=∞ forbids quantum corrections to the vacuum energy.
In the Gravity from Entropy framework, spherically symmetric black holes acquire r^{-4} corrections to Schwarzschild geometry, with large-mass evaporation at constant rate -β/24 and intermediate-mass loss following the classical Hawking M^{-2} scaling.
Exact 5D rotating Lifshitz black holes with electric and axionic charges were found and used to show that rotation weakens holographic superconductivity while higher z enhances it.
An improved heat kernel framework with phase-factor reconstruction computes symmetry-resolved entanglement entropy for charged systems and derives a cMERA flow equation that agrees with CFT and holographic calculations.
Holographic spacetime emerges as the 1-Wasserstein space of quantum state distributions under optimal transport, matching AdS2 black hole geometry in the SYK model and identified with generalized Krylov complexity.
In 2D centaur geometries the entropy difference of a modular-conjugate Hawking-pair probe traces an inverse mini-Page curve that bottoms at τ≈β/8, marking when information begins to leave the cosmological horizon.
A finite-dimensional regularized master field that minimizes residual loop equations reproduces exact Euclidean and perturbative Minkowski results for one- and two-matrix models.
Unitary QFTs are determined up to unitary isomorphism by closed-manifold partition functions; every reflection-positive partition function comes from a unitary QFT, so spatial wormholes do not break Hilbert-space factorization once the full charged spectrum is included.
Timelike geodesic-integrated Wightman functions in dS are dual to bulk-operator correlators with a linear combination of an OPE block and its Casimir partner.
Holographic dual of PT-symmetric BCFT via imaginary scalar on EOW brane shows spontaneous PT breaking and enhanced entanglement entropy growth in quenched state.
Constructs deformed vertex operators in a topological string description of T T-bar deformed tensionless AdS3/CFT2 and computes their exact tree-level two-point functions.
A construction assigns pure states to subregions in quantum gravity via partially frozen path integrals and gives a holographic prescription for their entanglement entropy that satisfies consistency conditions and recovers known formulas.
Modified entropy profiles from Barrow, Tsallis, Kaniadakis, logarithmic, and exponential entropies can serve as effective sources for traversable wormholes.
Effective dimension of Wasserstein space for quantum energy eigenstates reduces with increasing chaos, capturing Lyapunov exponents and indicating scar states via optimal transport geometry.
Two-loop 2- and 3-point functions of a massive 3d toy QFT with generalized conformal structure are log-finite in the deep IR, suggesting nonperturbative IR finiteness and, holographically, no cosmological singularity.
Brick-wall spectra in de Sitter space show long-range chaotic signatures via spectral form factor and Krylov complexity even when conventional level repulsion is absent.
The paper proposes that condensate competition in the 2d Gross-Neveu model generates an emergent AdS₃ bulk, a higher-spin tower, D1-branes, and linearized Einstein gravity with G₃ = ℓ_AdS/4πN².
The noise spectrum an interferometer would see from quantum spacetime jitter is computed for vacuum, thermal, squeezed, and scalar-backreaction states; all are Planck-suppressed.
A conformal map identifies the flat-space soft gluon S-algebra with light-ray operators built from CFT3 currents and their descendants in AdS4.
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.
Spectral functions of SYK, p-spin, and SU(M) Heisenberg models show exponential tails in spin-glass phases and quasiparticle families in spin-liquid phases, with a proof that exponential decay blocks detection of bulk causal structure.
Proposes that AdS3 gravity at finite cutoff is dual to a CFT2 coupled to timelike Liouville theory deformed by a marginal operator, with checks via semiclassical partition functions and EOM matching.
Establishes a holographic link between bulk gravitational radiation and dissipative corrections plus entropy production in boundary fluids, then constructs Carrollian analogues and celestial observables in the flat limit.
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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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Holograms and Standard Models
DSSYK∞ at infinite temperature duals in the flat-space limit to the 't Hooft model, and holographic entropy at TB=∞ forbids quantum corrections to the vacuum energy.
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Spherically symmetric black holes in Gravity from Entropy and spontaneous emission
In the Gravity from Entropy framework, spherically symmetric black holes acquire r^{-4} corrections to Schwarzschild geometry, with large-mass evaporation at constant rate -β/24 and intermediate-mass loss following the classical Hawking M^{-2} scaling.
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Novel five-dimensional rotating Lifshitz black holes with electric and axionic charges
Exact 5D rotating Lifshitz black holes with electric and axionic charges were found and used to show that rotation weakens holographic superconductivity while higher z enhances it.
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Symmetry-Resolved Entanglement Entropy from Heat Kernels
An improved heat kernel framework with phase-factor reconstruction computes symmetry-resolved entanglement entropy for charged systems and derives a cMERA flow equation that agrees with CFT and holographic calculations.
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Holography and Optimal Transport: Emergent Wasserstein Spacetime in Harmonic Oscillator, SYK and Krylov Complexity
Holographic spacetime emerges as the 1-Wasserstein space of quantum state distributions under optimal transport, matching AdS2 black hole geometry in the SYK model and identified with generalized Krylov complexity.
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The mini-Page Curve in Cosmology
In 2D centaur geometries the entropy difference of a modular-conjugate Hawking-pair probe traces an inverse mini-Page curve that bottoms at τ≈β/8, marking when information begins to leave the cosmological horizon.
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Regularized Master-Field Approximation for Large-$N$ Reduced Matrix Models
A finite-dimensional regularized master field that minimizes residual loop equations reproduces exact Euclidean and perturbative Minkowski results for one- and two-matrix models.
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Wormholes as red herrings: reflection positivity and the reconstruction of unitary quantum field theories
Unitary QFTs are determined up to unitary isomorphism by closed-manifold partition functions; every reflection-positive partition function comes from a unitary QFT, so spatial wormholes do not break Hilbert-space factorization once the full charged spectrum is included.
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CFT Dual for Timelike Geodesic in Lorentzian dS
Timelike geodesic-integrated Wightman functions in dS are dual to bulk-operator correlators with a linear combination of an OPE block and its Casimir partner.
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Holographic Dual of PT Symmetric BCFT
Holographic dual of PT-symmetric BCFT via imaginary scalar on EOW brane shows spontaneous PT breaking and enhanced entanglement entropy growth in quenched state.
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$\boldsymbol{T\overline{T}}$ correlators from tensionless strings
Constructs deformed vertex operators in a topological string description of T T-bar deformed tensionless AdS3/CFT2 and computes their exact tree-level two-point functions.
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Pure states for subregions in gravity and their entanglement entropy
A construction assigns pure states to subregions in quantum gravity via partially frozen path integrals and gives a holographic prescription for their entanglement entropy that satisfies consistency conditions and recovers known formulas.
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Traversable Wormholes Supported by Entropy-Inspired Effective Matter Sectors
Modified entropy profiles from Barrow, Tsallis, Kaniadakis, logarithmic, and exponential entropies can serve as effective sources for traversable wormholes.
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Wasserstein Space of Quantum Chaos
Effective dimension of Wasserstein space for quantum energy eigenstates reduces with increasing chaos, capturing Lyapunov exponents and indicating scar states via optimal transport geometry.
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3d QFT IR divergences as UV divergences in 4d Holographic Cosmology
Two-loop 2- and 3-point functions of a massive 3d toy QFT with generalized conformal structure are log-finite in the deep IR, suggesting nonperturbative IR finiteness and, holographically, no cosmological singularity.
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Cosmological brick walls & quantum chaotic dynamics of de Sitter horizons
Brick-wall spectra in de Sitter space show long-range chaotic signatures via spectral form factor and Krylov complexity even when conventional level repulsion is absent.
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Higher-spin composites and emergent AdS$_3$ geometry in the $(1+1)$-dimensional Gross-Neveu model
The paper proposes that condensate competition in the 2d Gross-Neveu model generates an emergent AdS₃ bulk, a higher-spin tower, D1-branes, and linearized Einstein gravity with G₃ = ℓ_AdS/4πN².
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Geometric noise spectrum in interferometers
The noise spectrum an interferometer would see from quantum spacetime jitter is computed for vacuum, thermal, squeezed, and scalar-backreaction states; all are Planck-suppressed.
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Soft Algebras in AdS$_4$ from Light Ray Operators in CFT$_3$
A conformal map identifies the flat-space soft gluon S-algebra with light-ray operators built from CFT3 currents and their descendants in AdS4.
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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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Searching for emergent spacetime in spin glasses
Spectral functions of SYK, p-spin, and SU(M) Heisenberg models show exponential tails in spin-glass phases and quasiparticle families in spin-liquid phases, with a proof that exponential decay blocks detection of bulk causal structure.
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Timelike Liouville theory and AdS$_3$ gravity at finite cutoff
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Radiation in Fluid/Gravity and the Flat Limit
Establishes a holographic link between bulk gravitational radiation and dissipative corrections plus entropy production in boundary fluids, then constructs Carrollian analogues and celestial observables in the flat limit.
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QFT in Klein space
Authors construct canonical and path-integral quantizations for QFT in Klein space using extra modes, deriving correlation functions that match Minkowski space via analytical continuation.
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Modular Channels, Thermal Filtering and the Spectral Emergence of Spacetime
Modular channels induce universal thermal filtering that explains Unruh and Page phenomena, reinterprets entanglement first law as Clausius relation to derive Einstein equations, and proposes MCFC linking causal screen area to filtered information storage.
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Carrollian Perspective on Celestial Holography
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Symmetry-resolved Krylov Complexity and the Uncoloured Tensor Model
In the Uncoloured Tensor Model, symmetry-resolved Krylov complexity matches the full operator complexity in some charge subspaces but not others, with the subspace-averaged value bounded above by the full-space value within computational limits.
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Equivariant Interpolations in Topological Holography
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An Interplay Between Fractional Calculus and Holographic Dark Energy
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The Entanglement Wedge Polygon
The entanglement wedge polygon volume is proposed as a holographic probe of multipartite entanglement; in AdS3 it is topologically quantized, and a mixed-state generalization is constructed.
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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.
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Bulk local states are built in flat holography via induced representations, with a dual basis resolving 3D bra-ket scaling issues and a tilde basis enabling explicit constructions in higher dimensions that recover the massive propagator.
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How to have your wormholes and factorize, too
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- Topics in Celestial holography: A bottom-up perspective
- Von Neumann Algebras in Double-Scaled SYK