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 Canonical reference
Solving the Schwarzian via the Conformal Bootstrap
Canonical reference. 100% of citing Pith papers cite this work as background.
14
Pith papers citing it
Background
100% of classified citations
abstract
We obtain exact expressions for a general class of correlation functions in the 1D quantum mechanical model described by the Schwarzian action, that arises as the low energy limit of the SYK model. The answer takes the form of an integral of a momentum space amplitude obtained via a simple set of diagrammatic rules. The derivation relies on the precise equivalence between the 1D Schwarzian theory and a suitable large $c$ limit of 2D Virasoro CFT. The mapping from the 1D to the 2D theory is similar to the construction of kinematic space. We also compute the out-of-time ordered four point function. The momentum space amplitude in this case contains an extra factor in the form of a crossing kernel, or R-matrix, given by a 6j-symbol of SU(1,1). We argue that the R-matrix describes the gravitational scattering amplitude near the horizon of an AdS${}_2$ black hole. Finally, we discuss the generalization of some of our results to ${\cal N}=1$ and ${\cal N}=2$ supersymmetric Schwarzian QM.
hub tools
citation-role summary
background 8
citation-polarity summary
roles
background 8polarities
background 8representative citing papers
Derives the all-order fluctuating hydrodynamics effective action and transport coefficients for the SYK lattice from its microscopic pseudo-Goldstone boson action.
Near-extremal charged black holes make decoherence of charged particle superpositions vanish at late times via a spin-induced energy gap from quantum metric fluctuations.
Projective geometry and Cayley transformations provide a common framework for the free particle-oscillator correspondences via the Schwarzian cocycle.
Summing non-perturbative contributions in the gravitational path integral, extended via matrix integral saddles including one- and two-eigenvalue instantons, resolves negativity of bulk entropies in two-sided black holes.
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.
Correlators of diverse models are expressed via universal formulae derived from a single defining function using KdV flows and the Gel'fand-Dikii equation.
The finite-cutoff JT gravity disk amplitude is reproduced via open-channel operators as a boundary-state matrix element, with the geodesic sector shown to be bandlimited and the branch-difference amplitude not equivalent to the thermal trace of any single lower-bounded β-independent Hamiltonian.
Constructs a phase space for gravitational degrees of freedom on null ray segments with commuting localized observables via edge modes and dressing time, then introduces an effective classical theory with Virasoro deformations to capture diffeomorphism anomalies and distinguish gauge, physical, and
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.
An SYK-based quantum system reproduces semiclassical correlators of quantum fields in rigid de Sitter space and non-trivial OTOC features including a doubled Lyapunov exponent.
Microscopic D-brane description of non-supersymmetric extremal black holes yields a unique ground state with non-zero energy, confirming absence of degeneracy.
A gapped parent Hamiltonian built from two copies of a target Hamiltonian plus ultra-local inter-copy couplings allows adiabatic preparation of high-fidelity thermofield double states for ETH-obeying systems.
Finite cutoff in JT gravity causes faster ERB-length saturation, deformation-dependent baby-universe emission only under Lorentzian evolution, and possible one-cut universality corrections in the matrix dual.
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.
-
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.
-
Not all black holes decohere quantum superpositions
Near-extremal charged black holes make decoherence of charged particle superpositions vanish at late times via a spin-induced energy gap from quantum metric fluctuations.
-
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.
-
Living on the edge: a non-perturbative resolution to the negativity of bulk entropies
Summing non-perturbative contributions in the gravitational path integral, extended via matrix integral saddles including one- and two-eigenvalue instantons, resolves negativity of bulk entropies in two-sided black holes.
-
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.
-
Universal formulae for correlators of a broad class of models
Correlators of diverse models are expressed via universal formulae derived from a single defining function using KdV flows and the Gel'fand-Dikii equation.
-
Open-Channel Operator Closure of the Finite-Cutoff JT Gravity Disk Amplitude
The finite-cutoff JT gravity disk amplitude is reproduced via open-channel operators as a boundary-state matrix element, with the geodesic sector shown to be bandlimited and the branch-difference amplitude not equivalent to the thermal trace of any single lower-bounded β-independent Hamiltonian.
-
Localization and anomalous reference frames in gravity
Constructs a phase space for gravitational degrees of freedom on null ray segments with commuting localized observables via edge modes and dressing time, then introduces an effective classical theory with Virasoro deformations to capture diffeomorphism anomalies and distinguish gauge, physical, and
-
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.
-
Towards a microscopic description of de Sitter dynamics
An SYK-based quantum system reproduces semiclassical correlators of quantum fields in rigid de Sitter space and non-trivial OTOC features including a doubled Lyapunov exponent.
-
An extremal black hole with a unique ground state
Microscopic D-brane description of non-supersymmetric extremal black holes yields a unique ground state with non-zero energy, confirming absence of degeneracy.
-
Preparing High-Fidelity Thermofield Double States
A gapped parent Hamiltonian built from two copies of a target Hamiltonian plus ultra-local inter-copy couplings allows adiabatic preparation of high-fidelity thermofield double states for ETH-obeying systems.
-
Finite cutoff JT gravity: Baby universes, Matrix dual, and (Krylov) Complexity
Finite cutoff in JT gravity causes faster ERB-length saturation, deformation-dependent baby-universe emission only under Lorentzian evolution, and possible one-cut universality corrections in the matrix dual.