Towards a Finite-$N$ Hologram

Abstract

We suggest that holographic tensor models related to SYK are viable candidates for exactly (ie., non-perturbatively in $N$) solvable holographic theories. The reason is that in these theories, the Hilbert space is a spinor representation, and the Hamiltonian (at least in some classes) can be arranged to commute with the Clifford level. This makes the theory solvable level by level. We demonstrate this for the specific case of the uncolored $O(n{)}^3$ tensor model with arbitrary even $n$, and reduce the question of determining the spectrum and eigenstates to an algebraic equation relating Young tableaux. Solving this reduced problem is conceptually trivial and amounts to matching the representations on either side, as we demonstrate explicitly at low levels. At high levels, representations become bigger, but should still be tractable. None of our arguments require any supersymmetry.

arXiv comment16 pages

References in corpus (45)

• A bound on chaos
• Eternal Black Holes in AdS
• Bubbling AdS space and 1/2 BPS geometries
• Chaos in AdS${}_2$ holography
• The Spectrum in the Sachdev-Ye-Kitaev Model
• Thermoelectric transport in disordered metals without quasiparticles: the SYK models and holography
• Local criticality, diffusion and chaos in generalized Sachdev-Ye-Kitaev models
• Fermionic Localization of the Schwarzian Theory
• Critical behavior of colored tensor models in the large N limit
• A toy model for the AdS/CFT correspondence
• A Generalization of Sachdev-Ye-Kitaev
• Strings from Tachyons
• Emergent Spacetime and Holographic CFTs
• The complete 1/N expansion of colored tensor models in arbitrary dimension
• Solvable model for a dynamical quantum phase transition from fast to slow scrambling
• Bi-Local Holography in the SYK Model
• The Bulk Dual of SYK: Cubic Couplings
• The 1/N expansion of colored tensor models in arbitrary dimension
• Analytical Spectral Density of the Sachdev-Ye-Kitaev Model at finite N
• The 1/N expansion of colored tensor models
• The complete $1/N$ expansion of a SYK--like tensor model
• Supersymmetric SYK model and random matrix theory
• Higher Dimensional Generalizations of the SYK Model
• A paradigm of open/closed duality: Liouville D-branes and the Kontsevich model
• Black Hole Collapse in the 1/c Expansion
• Quantum Chaos and Holographic Tensor Models
• Holographic description of quantum black hole on a computer
• $O(N)$ Random Tensor Models
• A Supersymmetric SYK-like Tensor Model
• Diagrammatics of a colored SYK model and of an SYK-like tensor model, leading and next-to-leading orders
• Very Long Time Scales and Black Hole Thermal Equilibrium
• Three Dimensional View of the SYK/AdS Duality
• AdS${}_2$ Holographic Dictionary
• Complete random matrix classification of SYK models with $\mathcal{N}=0$, $1$ and $2$ supersymmetry
• Tunable Quantum Chaos in the Sachdev-Ye-Kitaev Model Coupled to a Thermal Bath
• Nearly AdS2 Sugra and the Super-Schwarzian
• Random Matrices and Holographic Tensor Models
• Correlators in tensor models from character calculus
• Ward identities and combinatorics of rainbow tensor models
• SYK-like Tensor Models on the Lattice
• Vector models and generalized SYK models
• Rainbow tensor model with enhanced symmetry and extreme melonic dominance
• Black Hole Non-Formation in the Matrix Model
• Disorder in the Sachdev-Yee-Kitaev Model
• Comments on the Random Thirring Model

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• Menagerie of AdS${}_2$ boundary conditions
• Extremal and Near-Extremal Black Holes and Near-$CF{T}_1$
• Flat space holography and complex SYK
• Towards a bulk description of higher spin SYK
• 2PI effective action for the SYK model and tensor field theories
• Spectra of Eigenstates in Fermionic Tensor Quantum Mechanics
• The $1/N$ expansion of the symmetric traceless and the antisymmetric tensor models in rank three
• SYK Model, Chaos and Conserved Charge
• Phases Of Melonic Quantum Mechanics
• Contrasting SYK-like Models
• Tensor Models, Kronecker coefficients and Permutation Centralizer Algebras
• Towards the Holographic Dual of N = 2 SYK
• A Complex Fermionic Tensor Model in $d$ Dimensions
• Quantum criticality and duality in the SYK/AdS${}_2$ chain
• Supersymmetric Tensor Model at Large $N$ and Small $\epsilon$
• Spectrum of Majorana Quantum Mechanics with $O(4{)}^3$ Symmetry
• $\mathcal{N}=(0,2)$ SYK, Chaos and Higher-Spins
• Rotating Black Holes in AdS, Extremality and Chaos
• Majorana Fermion Quantum Mechanics for Higher Rank Tensors
• Probing typical black hole microstates
• On Melonic Supertensor Models
• Jackiw-Teitelboim Model Coupled to Conformal Matter in the Semi-Classical Limit
• Exact Solution of a Strongly Coupled Gauge Theory in 0+1 Dimensions
• Melonic Dominance in Subchromatic Sextic Tensor Models
• Gravitational collapse in SYK models and Choptuik-like phenomenon
• Late Time Quantum Chaos of pure states in the SYK model
• Chaotic Correlation Functions with Complex Fermions
• A Large-$N$ Phase Transition in a Finite Lattice Gauge Theory
• (Anti-)Symmetrizing Wave Functions