Gravitational null rays are quantized in a diffeomorphism-covariant way using the gravitational dressing time as quantum reference frame, producing a Virasoro crossed-product algebra of gauge-invariant observables.
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Witten,Gravity and the crossed product,JHEP10(2022) 008 [2112.12828]
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abstract
Recently Leutheusser and Liu [1,2] identified an emergent algebra of Type III$_1$ in the operator algebra of ${\mathcal N}=4$ super Yang-Mills theory for large $N$. Here we describe some $1/N$ corrections to this picture and show that the emergent Type III$_1$ algebra becomes an algebra of Type II$_\infty$. The Type II$_\infty$ algebra is the crossed product of the Type III$_1$ algebra by its modular automorphism group. In the context of the emergent Type II$_\infty$ algebra, the entropy of a black hole state is well-defined up to an additive constant, independent of the state. This is somewhat analogous to entropy in classical physics.
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representative citing papers
The DSSYK model emerges as the dynamics on the quantum homogeneous space of the von Neumann algebraic quantum group SU_q(1,1) ⋊ Z2.
No Rényi-type divergence obeying DPI, tensor additivity and matched cq conditioning admits a universal off-diagonal quantum focusing inequality.
An operator-algebraic quantization of the characteristic initial-value problem yields a candidate on-shell algebra for a gravitational subregion bounded by two null hypersurfaces.
Extends quantum reference frames to quantum reference fields in linearized quantum gravity and derives unitary maps implementing relational gauge-invariant observables between quantum perspectives.
The paper introduces a form-domain criterion and proves a sufficiency theorem that identifies which gapped observer sectors remain semiclassically admissible in Euclidean de Sitter gravity on the sphere.
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.
Defines a Type II₁ algebra of gravitationally dressed observables in de Sitter static patch whose entropy matches generalized entropy up to a state-independent additive constant.
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.
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.
Evanescent quantum extremal surfaces, bounded in area but not generalized entropy, diagnose failures of spacetime emergence in holography.
Modular Witten diagrams reproduce the O(λ² G_N) correction to holographic entanglement entropy, matching the canonical energy term in the quantum Ryu-Takayanagi formula with wedge shape deformation.
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.
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 a new large N limit dual to back-reacted traversable wormholes via algebra-at-infinity operators and algebraically reproduces the Maldacena-Stanford-Yang result on left-right observer effects.
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.
Reconstructs spacetime metric, curvature, and Einstein equations from matter field operator algebras in the G to 0 limit without using Bekenstein-Hawking area law, then models finite-N discrete spectra via random matrix completion of enlarged type III algebras.
Applies operational quantum reference frames to obtain type reduction for QFT algebras and to quantize boundary electric fluxes with gluing for quantum electromagnetism on spacetimes with boundaries.
An operator-algebraic definition of timelike entanglement entropy in QFT is shown to be real-valued via the timelike tube theorem.
Dressed relational observables imply quasi-de Sitter space corresponds to Type II_∞ von Neumann algebra with diverging trace in the gravity decoupling limit, unlike the finite-trace Type II_1 algebra for de Sitter space.
An Albert algebra description of the horizon yields a Volterra memory law on the Reissner-Nordstrom evaporation trajectory whose spectral overlap reconstructs the Page curve envelope without restoring standard AMPS tensor factorization.
citing papers explorer
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Gravitational null rays: Covariant Quantization and the Dressing Time
Gravitational null rays are quantized in a diffeomorphism-covariant way using the gravitational dressing time as quantum reference frame, producing a Virasoro crossed-product algebra of gauge-invariant observables.
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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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No off-diagonal quantum focusing for R\'enyi divergences
No Rényi-type divergence obeying DPI, tensor additivity and matched cq conditioning admits a universal off-diagonal quantum focusing inequality.
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Quantization of Gravity on Null Hypersurfaces
An operator-algebraic quantization of the characteristic initial-value problem yields a candidate on-shell algebra for a gravitational subregion bounded by two null hypersurfaces.
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Quantum Reference Fields Transformations in Linearized Quantum Gravity
Extends quantum reference frames to quantum reference fields in linearized quantum gravity and derives unitary maps implementing relational gauge-invariant observables between quantum perspectives.
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Spectral Admissibility of Real Observers in Euclidean de Sitter Gravity
The paper introduces a form-domain criterion and proves a sufficiency theorem that identifies which gapped observer sectors remain semiclassically admissible in Euclidean de Sitter gravity on the sphere.
-
q-Askey Deformations of Double-Scaled SYK
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.
-
An Algebra of Observables for de Sitter Space
Defines a Type II₁ algebra of gravitationally dressed observables in de Sitter static patch whose entropy matches generalized entropy up to a state-independent additive constant.
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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.
-
Wigner negativity in Krylov space and emergent semiclassicality
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.
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A Semiclassical Diagnostic for Spacetime Emergence
Evanescent quantum extremal surfaces, bounded in area but not generalized entropy, diagnose failures of spacetime emergence in holography.
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Modular Witten Diagrams and Quantum Extremality
Modular Witten diagrams reproduce the O(λ² G_N) correction to holographic entanglement entropy, matching the canonical energy term in the quantum Ryu-Takayanagi formula with wedge shape deformation.
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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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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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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.
-
Algebraic traversable wormholes
Proposes a new large N limit dual to back-reacted traversable wormholes via algebra-at-infinity operators and algebraically reproduces the Maldacena-Stanford-Yang result on left-right observer effects.
-
Fiducial observers and the thermal atmosphere in the black hole quantum throat
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.
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Spacetime from Operator Algebras
Reconstructs spacetime metric, curvature, and Einstein equations from matter field operator algebras in the G to 0 limit without using Bekenstein-Hawking area law, then models finite-N discrete spectra via random matrix completion of enlarged type III algebras.
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Quantum reference frames for spacetime symmetries and large gauge transformations
Applies operational quantum reference frames to obtain type reduction for QFT algebras and to quantize boundary electric fluxes with gluing for quantum electromagnetism on spacetimes with boundaries.
-
Timelike entanglement entropy Revisited
An operator-algebraic definition of timelike entanglement entropy in QFT is shown to be real-valued via the timelike tube theorem.
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Implication of dressed form of relational observable on von Neumann algebra
Dressed relational observables imply quasi-de Sitter space corresponds to Type II_∞ von Neumann algebra with diverging trace in the gravity decoupling limit, unlike the finite-trace Type II_1 algebra for de Sitter space.
-
Albertian Channel Memory in Black-Hole Evaporation
An Albert algebra description of the horizon yields a Volterra memory law on the Reissner-Nordstrom evaporation trajectory whose spectral overlap reconstructs the Page curve envelope without restoring standard AMPS tensor factorization.
- Semiclassical algebraic reconstruction for type III algebras
- Deforming the Double-Scaled SYK & Reaching the Stretched Horizon From Finite Cutoff Holography
- Von Neumann Algebras in Double-Scaled SYK