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.

arXiv comment61 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 (54)

• A bound on chaos
• Gapless Spin-Fluid Ground State in a Random Quantum Heisenberg Magnet
• Comments on the Sachdev-Ye-Kitaev model
• The Spectrum in the Sachdev-Ye-Kitaev Model
• Bekenstein-Hawking Entropy and Strange Metals
• Thermoelectric transport in disordered metals without quasiparticles: the SYK models and holography
• Local criticality, diffusion and chaos in generalized Sachdev-Ye-Kitaev models
• Diving into traversable wormholes
• Uncolored Random Tensors, Melon Diagrams, and the SYK Models
• Colored Tensor Models - a Review
• A Generalization of Sachdev-Ye-Kitaev
• The complete 1/N expansion of colored tensor models in arbitrary dimension
• Colored Group Field Theory
• Random tensor models in the large N limit: Uncoloring the colored tensor models
• Solvable model for a dynamical quantum phase transition from fast to slow scrambling
• Bi-Local Holography in the SYK Model
• More on Supersymmetric and 2d Analogs of the SYK Model
• The 1/N expansion of colored tensor models in arbitrary dimension
• The 1/N expansion of colored tensor models
• The complete $1/N$ expansion of a SYK--like tensor model
• Bounding the Space of Holographic CFTs with Chaos
• AdS_4/CFT_3 Construction from Collective Fields
• Supersymmetric SYK model and random matrix theory
• Higher Dimensional Generalizations of the SYK Model
• Large-N Collective Fields and Holography
• Quantum Chaos and Holographic Tensor Models
• Solvable Sachdev-Ye-Kitaev models in higher dimensions: from diffusion to many-body localization
• $O(N)$ Random Tensor Models
• Towards a 2d QFT Analog of the SYK Model
• Diagrammatics of a colored SYK model and of an SYK-like tensor model, leading and next-to-leading orders
• Three Dimensional View of the SYK/AdS Duality
• Complete random matrix classification of SYK models with $\mathcal{N}=0$, $1$ and $2$ supersymmetry
• Random Matrices and Holographic Tensor Models
• Correlators in tensor models from character calculus
• Ward identities and combinatorics of rainbow tensor models
• Correlators in the $\mathcal{N}=2$ Supersymmetric SYK Model
• Gauge Invariants, Correlators and Holography in Bosonic and Fermionic Tensor Models
• Conformal symmetry and its breaking in two dimensional Nearly Anti-de-Sitter space
• SYK-like Tensor Models on the Lattice
• Vector models and generalized SYK models
• Rainbow tensor model with enhanced symmetry and extreme melonic dominance
• 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
• Systematic $1/N$ corrections for bosonic and fermionic vector models without auxiliary fields
• Canonical Formulation of $O(N)$ Vector/Higher Spin Correspondence
• Comments on the Random Thirring Model
• Holography as a Gauge Phenomenon in Higher Spin Duality
• 1/N and Loop Corrections in Higher Spin AdS_4/CFT_3 Duality
• Conformality of $1/N$ corrections in SYK-like models
• Abelian Tensor Models on the Lattice
• Bulk from Bi-locals in Thermo Field CFT
• Thermofield Duality for Higher Spin Rindler Gravity
• The $ı\epsilon$ prescription in the SYK model

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• Towards the Holographic Dual of N = 2 SYK
• Quantum criticality and duality in the SYK/AdS${}_2$ chain
• Supersymmetric SYK Model with Global Symmetry
• Marginal Deformations and Rotating Horizons
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• From Kronecker to tableau pseudo-characters in tensor models
• Rotating Black Holes in AdS, Extremality and Chaos
• Non-local reparametrization action in coupled Sachdev-Ye-Kitaev models
• On Melonic Supertensor Models
• Invariant Operators, Orthogonal Bases and Correlators in General Tensor Models
• Exact Solution of a Strongly Coupled Gauge Theory in 0+1 Dimensions
• Tensor and Matrix models: a one-night stand or a lifetime romance?
• On 2D gauge theories in Jackiw-Teitelboim gravity
• Tensor Models for Black Hole Probes
• Chaos in Three-dimensional Higher Spin Gravity
• Classification of the quantum chaos in colored Sachdev-Ye-Kitaev models
• Note on global symmetry and SYK model
• Quantum Correction to Chaos in Schwarzian Theory
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• Near Conformal Perturbation Theory in SYK Type Models
• Spontaneous Symmetry Breaking in Tensor Theories
• Complete Solution of a Gauged Tensor Model
• Factorizing Wormholes in a Partially Disorder-Averaged SYK Model
• SYK Model with global symmetries in the double scaling limit
• Sign-Problem-Free Variant of Complex Sachdev-Ye-Kitaev Model
• Schwarzian for colored Jackiw-Teitelboim gravity
• New Limits for Large $N$ Matrix and Tensor Models: Large $D$, Melons and Applications
• Tensor Field Theories: Renormalization and Random Geometry
• A simple model for Hawking radiation
• Chiral symmetry breaking generalizes in tensor theories
• On the Explicit Asymptotic Symmetry Breaking of sl(3,R) Jackiw-Teitelboim Gravity
• A so(2,2) extension of JT gravity via the Virasoro-Kac-Moody semidirect product