The DSSYK model emerges as the dynamics on the quantum homogeneous space of the von Neumann algebraic quantum group SU_q(1,1) ⋊ Z2.
hub
Witten,Why Does Quantum Field Theory In Curved Spacetime Make Sense? And What Happens To The Algebra of Observables In The Thermodynamic Limit?, 2112.11614
12 Pith papers cite this work. Polarity classification is still indexing.
12
Pith papers citing it
abstract
This article aims to explain some of the basic facts about the questions raised in the title, without the technical details that are available in the literature. We provide a gentle introduction to some rather classical results about quantum field theory in curved spacetime and about the thermodynamic limit of quantum statistical mechanics. We also briefly explain that these results have an analog in the large N limit of gauge theory.
hub tools
citation-role summary
background 3
citation-polarity summary
roles
background 3polarities
background 3representative citing papers
Free Carrollian quantum field theories admit well-defined vacuum and KMS states via algebraic methods, with massless theories requiring nonregular states whose Hilbert spaces factorize into Fock and nonseparable zero-mode sectors relevant for flat space holography.
For zero-mean Gaussian states in free field theory, excitability from one state to another is equivalent to three explicit two-point-function conditions, and one-way excitability automatically implies two-way excitability (quasiequivalence).
New dynamical systems variables for coupled axion-saxion fields yield a general non-geodesicity expression at fixed points and identify genuinely non-geodesic attractors under exponential couplings.
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.
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.
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.
In this fuzzy-sphere matrix model the largest Lyapunov exponent drops to zero at finite temperature, respecting the Maldacena-Shenker-Stanford bound while entanglement shows fast scrambling.
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.
All separable Hilbert spaces of a given dimension are isomorphic, so there are only six basic coordinate operator types; their conjugate momenta form seven basic pairs via direct self-adjointness, self-adjoint extensions, or Neumark extensions.
citing papers explorer
-
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.
-
Carrollian quantum states and flat space holography
Free Carrollian quantum field theories admit well-defined vacuum and KMS states via algebraic methods, with massless theories requiring nonregular states whose Hilbert spaces factorize into Fock and nonseparable zero-mode sectors relevant for flat space holography.
-
Excitability in quantum field theory
For zero-mean Gaussian states in free field theory, excitability from one state to another is equivalent to three explicit two-point-function conditions, and one-way excitability automatically implies two-way excitability (quasiequivalence).
-
Extending the Dynamical Systems Toolkit: Coupled Fields in Multiscalar Dark Energy
New dynamical systems variables for coupled axion-saxion fields yield a general non-geodesicity expression at fixed points and identify genuinely non-geodesic attractors under exponential couplings.
-
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.
-
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.
-
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.
-
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.
-
Real-Time Quantum Dynamics on the Fuzzy Sphere: Chaos and Entanglement
In this fuzzy-sphere matrix model the largest Lyapunov exponent drops to zero at finite temperature, respecting the Maldacena-Shenker-Stanford bound while entanglement shows fast scrambling.
-
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.
-
All Hilbert spaces are the same: consequences for generalized coordinates and momenta
All separable Hilbert spaces of a given dimension are isomorphic, so there are only six basic coordinate operator types; their conjugate momenta form seven basic pairs via direct self-adjointness, self-adjoint extensions, or Neumark extensions.
- Von Neumann Algebras in Double-Scaled SYK