A Generalization of Sachdev-Ye-Kitaev

Abstract

The SYK model: fermions with a $q$-body, Gaussian-random, all-to-all interaction, is the first of a fascinating new class of solvable large $N$ models. We generalize SYK to include $f$ flavors of fermions, each occupying $N_a$ sites and appearing with a $q_a$ order in the interaction. Like SYK, this entire class of models generically has an infrared fixed point. We compute the infrared dimensions of the fermions, and the spectrum of singlet bilinear operators. We show that there is always a dimension-two operator in the spectrum, which implies that, like in SYK, there is breaking of conformal invariance and maximal chaos in the infrared four-point function of the generalized model. After a disorder average, the generalized model has a global $O(N_1)\times O(N_2)\times \dots \times O(N_f)$ symmetry: a subgroup of the $O(N)$ symmetry of SYK; thereby giving a richer spectrum. We also elucidate aspects of the large $q$ limit and the OPE, and solve $q=2$ SYK at finite $N$.

46 pages, v2 minor changes; published version

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Cited by in corpus (40)

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• Spread of entanglement in a Sachdev-Ye-Kitaev chain
• Bosonic Tensor Models at Large $N$ and Small $\epsilon$
• Complete random matrix classification of SYK models with $\mathcal{N}=0$, $1$ and $2$ supersymmetry
• Dispersive SYK model: band structure and quantum chaos
• Menagerie of AdS${}_2$ boundary conditions
• Tunable Quantum Chaos in the Sachdev-Ye-Kitaev Model Coupled to a Thermal Bath
• Correlators in tensor models from character calculus
• SYK Models and SYK-like Tensor Models with Global Symmetry
• Correlators in the $\mathcal{N}=2$ Supersymmetric SYK Model
• A line of CFTs: from generalized free fields to SYK
• On the Chaos Bound in Rotating Black Holes
• Symmetry Breaking in Coupled SYK or Tensor Models
• A note on the SYK model with complex fermions
• SYK Model, Chaos and Conserved Charge
• On Large $N$ Limit of Symmetric Traceless Tensor Models
• Supersymmetric SYK Model: Bi-local Collective Superfield/Supermatrix Formulation
• Phases Of Melonic Quantum Mechanics
• Diffusion in higher dimensional SYK model with complex fermions
• The $1/N$ expansion of tensor models with two symmetric tensors
• Non-Gaussian disorder average in the Sachdev-Ye-Kitaev model
• Constructing AdS_2 flow geometries
• Towards a Finite-$N$ Hologram
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• Supersymmetry breaking and Nambu-Goldstone fermions with cubic dispersion
• Marginal Deformations and Rotating Horizons
• Two-point Functions in a Holographic Kondo Model
• Excitation spectra of quantum matter without quasiparticles II: random $t$-$J$ models
• Note on global symmetry and SYK model
• Generalized cut operation associated with higher order variation in tensor models
• Transport properties of an interacting Majorana chain
• Spatial regions, chaos bound and its violation
• SYK Model with global symmetries in the double scaling limit
• Nearly AdS${}_2$ holography in quantum CGHS model
• New Limits for Large $N$ Matrix and Tensor Models: Large $D$, Melons and Applications
• The quantum $p$-spin glass model: A user manual for holographers
• Holographic JT gravity with quartic couplings