Higher Dimensional Generalizations of the SYK Model

Abstract

We discuss a 1+1 dimensional generalization of the Sachdev-Ye-Kitaev model. The model contains $N$ Majorana fermions at each lattice site with a nearest-neighbour hopping term. The SYK random interaction is restricted to low momentum fermions of definite chirality within each lattice site. This gives rise to an ordinary 1+1 field theory above some energy scale and a low energy SYK-like behavior. We exhibit a class of low-pass filters which give rise to a rich variety of hyperscaling behaviour in the IR. We also discuss another set of generalizations which describes probing an SYK system with an external fermion, together with the new scaling behavior they exhibit in the IR.

23 pages, 3 figures. Minor changes

References in corpus (4)

• An Investigation of AdS${}_2$ Backreaction and Holography
• AdS${}_2$ Holographic Dictionary
• Black Holes, Entanglement and Random Matrices
• Chiral 2D "Strange Metals" from N = 4 SYM

Cited by in corpus (16)

• More on Supersymmetric and 2d Analogs of the SYK Model
• Three Dimensional View of the SYK/AdS Duality
• Spread of entanglement in a Sachdev-Ye-Kitaev chain
• Eigenstate thermalization in the Sachdev-Ye-Kitaev model
• Complete random matrix classification of SYK models with $\mathcal{N}=0$, $1$ and $2$ supersymmetry
• Dispersive SYK model: band structure and quantum chaos
• Tunable Quantum Chaos in the Sachdev-Ye-Kitaev Model Coupled to a Thermal Bath
• Menagerie of AdS${}_2$ boundary conditions
• SYK Models and SYK-like Tensor Models with Global Symmetry
• Correlators in the $\mathcal{N}=2$ Supersymmetric SYK Model
• SYK Model, Chaos and Conserved Charge
• Supersymmetric SYK Model: Bi-local Collective Superfield/Supermatrix Formulation
• Diffusion in higher dimensional SYK model with complex fermions
• Towards a Finite-$N$ Hologram
• Two-point Functions in a Holographic Kondo Model
• Solvable model for quantum criticality between Sachdev-Ye-Kitaev liquid and disordered Fermi liquid