Multi-trace Correlators in the SYK Model and Non-geometric Wormholes

Abstract

We consider multi-energy level distributions in the SYK model, and in particular, the role of global fluctuations in the density of states of the SYK model. The connected contributions to the moments of the density of states go to zero as $N\to \infty$, however, they are much larger than the standard RMT correlations. We provide a diagrammatic description of the leading behavior of these connected moments, showing that the dominant diagrams are given by 1PI cactus graphs, and derive a vector model of the couplings which reproduces these results. We generalize these results to the first subleading corrections, and to fluctuations of correlation functions. In either case, the new set of correlations between traces (i.e. between boundaries) are not associated with, and are much larger than, the ones given by topological wormholes. The connected contributions that we discuss are the beginning of an infinite series of terms, associated with more and more information about the ensemble of couplings, which hints towards the dual of a single realization. In particular, we suggest that incorporating them in the gravity description requires the introduction of new, lighter and lighter, fields in the bulk with fluctuating boundary couplings.

arXiv comment81 pages, 23 figures. V2: added short discussion on the modified dip time, and corrected minor typos

References in corpus (58)

• Chaos and Quantum Thermalization
• A bound on chaos
• Random Matrix Theories in Quantum Physics: Common Concepts
• Gapless Spin-Fluid Ground State in a Random Quantum Heisenberg Magnet
• Comments on the Sachdev-Ye-Kitaev model
• Black holes and the butterfly effect
• Replica Wormholes and the Entropy of Hawking Radiation
• Chaos in AdS${}_2$ holography
• The Spectrum in the Sachdev-Ye-Kitaev Model
• The soft mode in the Sachdev-Ye-Kitaev model and its gravity dual
• Fermionic Localization of the Schwarzian Theory
• Spectral and thermodynamic properties of the Sachdev-Ye-Kitaev model
• Sachdev-Ye-Kitaev Model as Liouville Quantum Mechanics
• Transcending the ensemble: baby universes, spacetime wormholes, and the order and disorder of black hole information
• Solving the Schwarzian via the Conformal Bootstrap
• A universal result on central charges in the presence of double-trace deformations
• JT gravity as a matrix integral
• A semiclassical ramp in SYK and in gravity
• Sachdev-Ye-Kitaev Model and Thermalization on the Boundary of Many-Body Localized Fermionic Symmetry Protected Topological States
• "Double-trace" Deformations, Boundary Conditions and Spacetime Singularities
• Power-law out of time order correlation functions in the SYK model
• Notes on the complex Sachdev-Ye-Kitaev model
• Spectral form factor in a random matrix theory
• Analytical Spectral Density of the Sachdev-Ye-Kitaev Model at finite N
• Towards a full solution of the large N double-scaled SYK model
• The path integral of 3D gravity near extremality; or, JT gravity with defects as a matrix integral
• An introduction to the SYK model
• Multiple-Trace Operators and Non-Local String Theories
• All point correlation functions in SYK
• Gravity/Ensemble Duality
• Supersymmetric SYK model and random matrix theory
• Scrambling the spectral form factor: unitarity constraints and exact results
• Double-trace operators and one-loop vacuum energy in AdS/CFT
• Eigenstate Thermalization and Disorder Averaging in Gravity
• Many-Body Chaos in the Sachdev-Ye-Kitaev Model
• Chord diagrams, exact correlators in spin glasses and black hole bulk reconstruction
• Spectral form factors and late time quantum chaos
• Observations of Hawking radiation: the Page curve and baby universes
• Phase Transition in the Density of States of Quantum Spin Glasses
• Late Time Correlation Functions, Baby Universes, and ETH in JT Gravity
• Free Energy from Replica Wormholes
• Quantum ergodicity in the SYK model
• Universal low temperature theory of charged black holes with AdS${}_2$ horizons
• Complete random matrix classification of SYK models with $\mathcal{N}=0$, $1$ and $2$ supersymmetry
• The double scaled limit of Super--Symmetric SYK models
• Exact moments of the Sachdev-Ye-Kitaev model up to order $1/N^2$
• Wormholes without averaging
• Periodic Table of SYK and supersymmetric SYK
• Spectral Fluctuations in the Sachdev-Ye-Kitaev Model
• Replica-nondiagonal solutions in the SYK model
• Complex Sachdev-Ye-Kitaev model in the double scaling limit
• Supersymmetry in the nonsupersymmetric Sachdev-Ye-Kitaev model
• On the replica structure of Sachdev-Ye-Kitaev model
• Large $N$ expansion of the moments and free energy of Sachdev-Ye-Kitaev model, and the enumeration of intersection graphs
• Supersymmetry method for interacting chaotic and disordered systems: the SYK model
• Spectral form factor in the double-scaled SYK model
• Towards a String Dual of SYK
• Spectrum of SYK model II: Central limit theorem

Cited by in corpus (2)

• Universality and its limits in non-Hermitian many-body quantum chaos using the Sachdev-Ye-Kitaev model
• Wormhole calculus without averaging from $O(N{)}^{q-1}$ tensor model