Three Dimensional View of the SYK/AdS Duality

Abstract

We show that the spectrum of the SYK model can be interpreted as that of a 3D scalar coupled to gravity. The scalar has a mass which is at the Breitenholer-Freedman bound of AdS${}_2$, and subject to a delta function potential at the center of the interval along the third direction. This, through Kaluza-Klein procedure on AdS${}_2\times (S^1)/Z_2$, generates the spectrum reproducing the bi-local propagator at strong coupling. Furthermore, the leading $1/J$ correction calculated in this picture reproduces the known correction to the poles of the SYK propagator, providing credence to a conjecture that the bulk dual of this model can be interpreted as a three dimensional theory.

19 pages; v2: further clarifications and references added

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Cited by in corpus (14)

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• Eigenstate thermalization in the Sachdev-Ye-Kitaev model
• Dispersive SYK model: band structure and quantum chaos
• SYK Models and SYK-like Tensor Models with Global Symmetry
• Correlators in the $\mathcal{N}=2$ Supersymmetric SYK Model
• On the Chaos Bound in Rotating Black Holes
• Evaporation dynamics of the Sachdev-Ye-Kitaev model
• Supersymmetric SYK Model: Bi-local Collective Superfield/Supermatrix Formulation
• Phases Of Melonic Quantum Mechanics
• Towards a Finite-$N$ Hologram
• Observing black holes through holographic superconductors
• The Cosmological OTOC: A New Proposal for Quantifying Auto-Correlated Random Non-Chaotic Primordial Fluctuations
• Holography for Tensor models
• Holographic JT gravity with quartic couplings