The Bulk Dual of SYK: Cubic Couplings

Abstract

The SYK model, a quantum mechanical model of $N\gg 1$ Majorana fermions ${\chi }_i$, with a $q$-body, random interaction, is a novel realization of holography. It is known that the AdS${}_2$ dual contains a tower of massive particles, yet there is at present no proposal for the bulk theory. As SYK is solvable in the $1/N$ expansion, one can systematically derive the bulk. We initiate such a program, by analyzing the fermion two, four and six-point functions, from which we extract the tower of singlet, large $N$ dominant, operators, their dimensions, and their three-point correlation functions. These determine the masses of the bulk fields and their cubic couplings. We present these couplings, analyze their structure and discuss the simplifications that arise for large $q$.

39 pages, v2: Evaluation of integral in Sec. 3.3.2 corrected

References in corpus (25)

• An Investigation of AdS${}_2$ Backreaction and Holography
• Thermoelectric transport in disordered metals without quasiparticles: the SYK models and holography
• Uncolored Random Tensors, Melon Diagrams, and the SYK Models
• Spectral and thermodynamic properties of the Sachdev-Ye-Kitaev model
• A Generalization of Sachdev-Ye-Kitaev
• Sachdev-Ye-Kitaev Model as Liouville Quantum Mechanics
• Analytical Spectral Density of the Sachdev-Ye-Kitaev Model at finite N
• The 1/N expansion of colored tensor models
• Supersymmetric SYK model and random matrix theory
• Higher Dimensional Generalizations of the SYK Model
• Quantum Chaos and Holographic Tensor Models
• Towards a 2d QFT Analog of the SYK Model
• Diagrammatics of a colored SYK model and of an SYK-like tensor model, leading and next-to-leading orders
• A Supersymmetric SYK-like Tensor Model
• Instability of the non-Fermi liquid state of the Sachdev-Ye-Kitaev Model
• Spinning Witten Diagrams
• Strange metals and the AdS/CFT correspondence
• Echoes of chaos from string theory black holes
• Disorder in the Sachdev-Yee-Kitaev Model
• Supersymmetry breaking and Nambu-Goldstone fermions with cubic dispersion
• Two-point Functions in a Holographic Kondo Model
• The importance of the Selberg integral
• Solvable Quantum Grassmann Matrices
• Dynamical thermalization in isolated quantum dots and black holes
• Decoherence and Microscopic Diffusion at SYK

Cited by in corpus (126)

• The soft mode in the Sachdev-Ye-Kitaev model and its gravity dual
• AdS${}_2$ holography and the SYK model
• On the Dynamics of Near-Extremal Black Holes
• Towards a full solution of the large N double-scaled SYK model
• An introduction to the SYK model
• All point correlation functions in SYK
• $d$-dimensional SYK, AdS Loops, and $6j$ Symbols
• The Schwarzian Theory - Origins
• Solvable Sachdev-Ye-Kitaev models in higher dimensions: from diffusion to many-body localization
• The Schwarzian Theory - A Wilson Line Perspective
• Approximating the Sachdev-Ye-Kitaev model with Majorana wires
• Chord diagrams, exact correlators in spin glasses and black hole bulk reconstruction
• Three Dimensional View of the SYK/AdS Duality
• Eigenstate thermalization in the Sachdev-Ye-Kitaev model
• Defects in Jackiw-Teitelboim Quantum Gravity
• Notes on Melonic $O(N{)}^{q-1}$ Tensor Models
• Phase Diagram of Planar Matrix Quantum Mechanics, Tensor, and Sachdev-Ye-Kitaev Models
• Spinning Witten Diagrams
• Symmetries Near the Horizon
• Dispersive SYK model: band structure and quantum chaos
• Jackiw-Teitelboim Gravity and Rotating Black Holes
• Menagerie of AdS${}_2$ boundary conditions
• Extremal and Near-Extremal Black Holes and Near-$CF{T}_1$
• Tunable Quantum Chaos in the Sachdev-Ye-Kitaev Model Coupled to a Thermal Bath
• Flat space holography and complex SYK
• Nearly AdS2 Sugra and the Super-Schwarzian
• Random Matrices and Holographic Tensor Models
• Correlators in tensor models from character calculus
• Fine Structure of Jackiw-Teitelboim Quantum Gravity
• Ward identities and combinatorics of rainbow tensor models
• Space-Time in the SYK Model
• Correlators in the $\mathcal{N}=2$ Supersymmetric SYK Model
• A line of CFTs: from generalized free fields to SYK
• Three Dimensional View of Arbitrary $q$ SYK models
• Quantum Simulation of the Non-Fermi-Liquid State of Sachdev-Ye-Kitaev Model
• Towards a bulk description of higher spin SYK
• 2PI effective action for the SYK model and tensor field theories
• Evaporation dynamics of the Sachdev-Ye-Kitaev model
• Chaotic scattering of highly excited strings
• Rainbow tensor model with enhanced symmetry and extreme melonic dominance
• Clocks and Rods in Jackiw-Teitelboim Quantum Gravity
• The double scaled limit of Super--Symmetric SYK models
• Supersymmetric SYK Model: Bi-local Collective Superfield/Supermatrix Formulation
• Pedagogical introduction to SYK model and 2D Dilaton Gravity
• Crossing symmetry, transcendentality and the Regge behaviour of 1d CFTs
• Diffusion in higher dimensional SYK model with complex fermions
• Structure Constants of Defect Changing Operators on the 1/2 BPS Wilson Loop
• Phases Of Melonic Quantum Mechanics
• Dynamical actions and q-representation theory for double-scaled SYK
• The $1/N$ expansion of tensor models with two symmetric tensors
• From Coxeter Higher-Spin Theories to Strings and Tensor Models
• Cut and join operator ring in Aristotelian tensor model
• Excitation spectra of quantum matter without quasiparticles I: Sachdev-Ye-Kitaev models
• Traversable wormhole and Hawking-Page transition in coupled complex SYK models
• Towards the Holographic Dual of N = 2 SYK
• Constructing AdS_2 flow geometries
• A Complex Fermionic Tensor Model in $d$ Dimensions
• Towards a Finite-$N$ Hologram
• Quantum criticality and duality in the SYK/AdS${}_2$ chain
• Spontaneous Breaking of $U(1)$ Symmetry in Coupled Complex SYK Models
• Supersymmetric SYK Model with Global Symmetry
• Topological Sachdev-Ye-Kitaev Model
• Complex Sachdev-Ye-Kitaev model in the double scaling limit
• The Cosmological OTOC: Formulating new cosmological micro-canonical correlation functions for random chaotic fluctuations in Out-of-Equilibrium Quantum Statistical Field Theory
• A One-Loop Test of the near-AdS${}_2$/near-CFT${}_1$ Correspondence
• Thickening and sickening the SYK model
• From Kronecker to tableau pseudo-characters in tensor models
• $\mathcal{N}=(0,2)$ SYK, Chaos and Higher-Spins
• Rotating Black Holes in AdS, Extremality and Chaos
• JT gravity and the models of Hawking-Page transition for 2D black holes
• Quantum Out-of-Equilibrium Cosmology
• Rotating 5D Black Holes: Interactions and deformations near extremality
• On the replica structure of Sachdev-Ye-Kitaev model
• Conformality of $1/N$ corrections in SYK-like models
• On Melonic Supertensor Models
• Quantum chaos without false positives
• Generalized conformal structure, dilaton gravity and SYK
• Jackiw-Teitelboim Model Coupled to Conformal Matter in the Semi-Classical Limit
• Melonic Dominance in Subchromatic Sextic Tensor Models
• Weyl transformation and regular solutions in a deformed Jackiw-Teitelboim model
• Eigenstate Thermalisation in the conformal Sachdev-Ye-Kitaev model: an analytic approach
• Colored discrete spaces: higher dimensional combinatorial maps and quantum gravity
• Size of bulk fermions in the SYK model
• Page Curve from Non-Markovianity
• Rescuing a black hole in the large-$q$ coupled SYK model
• Correlation functions in the Schwarzian theory
• Global phase diagram of the one-dimensional Sachdev-Ye-Kitaev model at finite $N$
• Chiral Algebras of Two-Dimensional SYK Models
• Tensor Models for Black Hole Probes
• Notes on the SYK model in real time
• The Cosmological OTOC: A New Proposal for Quantifying Auto-Correlated Random Non-Chaotic Primordial Fluctuations
• Schwarzian correction to quantum correlation in SYK model
• Spectrum of a Gross-Neveu Yukawa model with flavor disorder in $d=3$
• $Ad{S}_2$ holography and ModMax
• Revisiting Extremal Couplings in AdS/CFT
• Unusual view of the Schwarzian theory
• $SO(3)$-invariant phase of the $O(N{)}^3$ tensor model
• Schwarzian functional integrals calculus
• On 1D, N = 4 Supersymmetric SYK-Type Models (I)
• Near Conformal Perturbation Theory in SYK Type Models
• Models of phase stability in Jackiw-Teitelboim gravity
• The Schwarzian sector of higher spin CFTs
• Generalized cut operation associated with higher order variation in tensor models
• SYK/AdS duality with Yang-Baxter deformations
• Entropy Linear Response Theory with Non-Markovian Bath
• N=4 SYM Quantum Spectral Curve in BFKL regime
• On 1/N diagrammatics in the SYK model beyond the conformal limit
• Simple rules of functional integration in the Schwarzian theory: SYK correlators
• Bulk Reconstruction from Generalized Free Fields
• True SYK or (con)sequences
• Chaotic Correlation Functions with Complex Fermions
• Phase space holography with no strings attached
• SYK does not Transit Gloria Mundi just yet
• SYK Model with global symmetries in the double scaling limit
• Quantum Chaos, Thermodynamics and Black Hole Microstates in the mass deformed SYK model
• Precise Low-Temperature Expansions for the Sachdev-Ye-Kitaev model
• Super-maximal chaos and instability
• Sextic tensor field theories in rank $3$ and $5$
• The quantum $p$-spin glass model: A user manual for holographers
• Tensor Field Theories: Renormalization and Random Geometry
• A simple model for Hawking radiation
• Holographic central charge for sine dilaton gravity
• Nearly AdS${}_2$ holography in quantum CGHS model
• AdS${}_3$/AdS${}_2$ degression of massless particles
• Holographic JT gravity with quartic couplings
• Matter Coupling of Dirac Matter in the Context of the SYK Model: Non-Gaussian Random Couplings and Bulk Mass Deformations