A Note on Sachdev-Ye-Kitaev Like Model without Random Coupling

Abstract

We study a description of the large N limit of the Sachdev-Ye-Kitaev (SYK) model in terms of quantum mechanics without quenched disorder. Instead of random couplings, we introduce massive scalar fields coupled to fermions, and study a small mass limit of the theory. We show that, under a certain condition, the correlation functions of fermions reproduce those of the SYK model with a temperature dependent coupling constant in the large N limit. We also discuss a supersymmetric generalization of our quantum mechanical model. As a byproduct, we develop an efficient way of estimating the large N behavior of correlators in the SYK model.

19 pages, 8 figures, references added

References in corpus (11)

• Comments on the Sachdev-Ye-Kitaev model
• Chaos in AdS${}_2$ holography
• An Investigation of AdS${}_2$ Backreaction and Holography
• Uncolored Random Tensors, Melon Diagrams, and the SYK Models
• Spectral and thermodynamic properties of the Sachdev-Ye-Kitaev model
• Sachdev-Ye-Kitaev Model as Liouville Quantum Mechanics
• Numerical study of fermion and boson models with infinite-range random interactions
• The complete $1/N$ expansion of a SYK--like tensor model
• Digital Quantum Simulation of Minimal AdS/CFT
• Conformal symmetry and its breaking in two dimensional Nearly Anti-de-Sitter space
• Bi-Local Holography in the SYK Model: Perturbations

Cited by in corpus (13)

• Analytical Spectral Density of the Sachdev-Ye-Kitaev Model at finite N
• Supersymmetric SYK model and random matrix theory
• A Supersymmetric SYK-like Tensor Model
• Phase Diagram of Planar Matrix Quantum Mechanics, Tensor, and Sachdev-Ye-Kitaev Models
• Competition between Chaotic and Non-Chaotic Phases in a Quadratically Coupled Sachdev-Ye-Kitaev Model
• Tunable Quantum Chaos in the Sachdev-Ye-Kitaev Model Coupled to a Thermal Bath
• Random Matrices and Holographic Tensor Models
• Correlators in the $\mathcal{N}=2$ Supersymmetric SYK Model
• SYK Model, Chaos and Conserved Charge
• Supersymmetric SYK Model: Bi-local Collective Superfield/Supermatrix Formulation
• Comments on 2D dilaton gravity system with a hyperbolic dilaton potential
• Deformations of the Almheiri-Polchinski model
• Complete Solution of a Gauged Tensor Model