SYK Models and SYK-like Tensor Models with Global Symmetry

Abstract

In this paper, we study an SYK model and an SYK-like tensor model with global symmetry. First, we study the large $N$ expansion of the bi-local collective action for the SYK model with manifest global symmetry. We show that the global symmetry is enhanced to a local symmetry at strong coupling limit, and the corresponding symmetry algebra is the Kac-Moody algebra. The emergent local symmetry together with the emergent reparametrization is spontaneously and explicit broken. This leads to a low energy effective action. We evaluate four point functions, and obtain spectrum of our model. We derive the low energy effective action and analyze the chaotic behavior of the four point functions. We also consider the recent 3D gravity conjecture for our model. We also introduce an SYK-like tensor model with global symmetry. We first study chaotic behavior of four point functions in various channels for the rank-3 case, and generalize this into a rank-$(q-1)$ tensor model.

61 pages, 8 figures; v2: typos corrected, references added, appendix D revised; v3: typos corrected, 1 figure added for clarification, substantial revisions and clarifications (conclusions unchanged)

References in corpus (17)

• Uncolored Random Tensors, Melon Diagrams, and the SYK Models
• A Generalization of Sachdev-Ye-Kitaev
• Random tensor models in the large N limit: Uncoloring the colored tensor models
• More on Supersymmetric and 2d Analogs of the SYK Model
• The 1/N expansion of colored tensor models
• The complete $1/N$ expansion of a SYK--like tensor model
• AdS_4/CFT_3 Construction from Collective Fields
• Higher Dimensional Generalizations of the SYK Model
• Three Dimensional View of the SYK/AdS Duality
• Complete random matrix classification of SYK models with $\mathcal{N}=0$, $1$ and $2$ supersymmetry
• Correlators in tensor models from character calculus
• Correlators in the $\mathcal{N}=2$ Supersymmetric SYK Model
• Gauge Invariants, Correlators and Holography in Bosonic and Fermionic Tensor Models
• On Large $N$ Limit of Symmetric Traceless Tensor Models
• Supersymmetric SYK Model: Bi-local Collective Superfield/Supermatrix Formulation
• The $1/N$ expansion of tensor models with two symmetric tensors
• Holography as a Gauge Phenomenon in Higher Spin Duality

Cited by in corpus (6)

• Gauge Invariants, Correlators and Holography in Bosonic and Fermionic Tensor Models
• On the Chaos Bound in Rotating Black Holes
• Phases Of Melonic Quantum Mechanics
• Marginal Deformations and Rotating Horizons
• Note on global symmetry and SYK model
• New Limits for Large $N$ Matrix and Tensor Models: Large $D$, Melons and Applications