Supersymmetric SYK Model: Bi-local Collective Superfield/Supermatrix Formulation

Abstract

We discuss the bi-local collective theory for the $\mathcal{N}=1,2$ supersymmetric Sachdev-Ye-Kitaev (SUSY SYK) models. We construct a bi-local superspace, and formulate the bi-local collective superfield theory of the one-dimensional SUSY vector model. The bi-local collective theory provides systematic analysis of the SUSY SYK models. We find that this bi-local collective theory naturally leads to supermatrix formulation in the bi-local superspace. This supermatrix formulation drastically simplifies the analysis of the SUSY SYK models. We also study $\mathcal{N}=1$ bi-local superconformal generators in the supermatrix formulation, and find the eigenvectors of teh superconformal Casimir. We diagonalize the quadratic action in large $N$ expansion.

arXiv comment48 page; v2:typo corrected, reference added, notation for the eigenfunctions changed

References in corpus (70)

• A bound on chaos
• Gapless Spin-Fluid Ground State in a Random Quantum Heisenberg Magnet
• Comments on the Sachdev-Ye-Kitaev model
• Black holes and the butterfly effect
• Chaos in AdS${}_2$ holography
• The Spectrum in the Sachdev-Ye-Kitaev Model
• Localized shocks
• Black Holes and Random Matrices
• Bekenstein-Hawking Entropy and Strange Metals
• Thermoelectric transport in disordered metals without quasiparticles: the SYK models and holography
• Delta M_K and epsilon_K in SUSY at the Next-to-Leading order
• Holographic metals and the fractionalized Fermi liquid
• Local criticality, diffusion and chaos in generalized Sachdev-Ye-Kitaev models
• Fermionic Localization of the Schwarzian Theory
• Uncolored Random Tensors, Melon Diagrams, and the SYK Models
• Spectral and thermodynamic properties of the Sachdev-Ye-Kitaev model
• A Generalization of Sachdev-Ye-Kitaev
• Solving the Schwarzian via the Conformal Bootstrap
• Non-Fermi liquid regime of a doped Mott insulator
• Quantum Fluctuations of a Nearly Critical Heisenberg Spin Glass
• 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 Bulk Dual of SYK: Cubic Couplings
• One Loop Tests of Higher Spin AdS/CFT
• Mean-Field Theory of a Quantum Heisenberg Spin Glass
• The complete $1/N$ expansion of a SYK--like tensor model
• 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
• Towards a 2d QFT Analog of the SYK Model
• A Supersymmetric SYK-like Tensor 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
• Energy diffusion and the butterfly effect in inhomogeneous Sachdev-Ye-Kitaev chains
• Higher Spin AdS${}_{d+1}$/CFT${}_d$ at One Loop
• Partition Functions and Casimir Energies in Higher Spin AdS_{d+1}/CFT_d
• Complete random matrix classification of SYK models with $\mathcal{N}=0$, $1$ and $2$ supersymmetry
• Tunable Quantum Chaos in the Sachdev-Ye-Kitaev Model Coupled to a Thermal Bath
• Nearly AdS2 Sugra and the Super-Schwarzian
• Random Matrices and Holographic Tensor Models
• Correlators in tensor models from character calculus
• Developments in 2D String Theory
• Ward identities and combinatorics of rainbow tensor models
• Correlators in the $\mathcal{N}=2$ Supersymmetric SYK Model
• SYK-like Tensor Models on the Lattice
• Rainbow tensor model with enhanced symmetry and extreme melonic dominance
• Vector models and generalized SYK models
• On Large $N$ Limit of Symmetric Traceless Tensor Models
• Collective String Field Theory of Matrix Models in the BMN Limit
• Systematic $1/N$ corrections for bosonic and fermionic vector models without auxiliary fields
• Bi-local Construction of Sp(2N)/dS 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
• The Exact Solution of the Schwarzian Theory
• Collective field theory of the matrix-vector model
• Conformality of $1/N$ corrections in SYK-like models
• Marinari-Parisi and Supersymmetric Collective Field Theory
• Abelian Tensor Models on the Lattice
• Bulk from Bi-locals in Thermo Field CFT
• Perturbative and Non-Perturbative Aspects in Vector Model/Higher Spin Duality
• A Note on Sachdev-Ye-Kitaev Like Model without Random Coupling
• Bi-local Model of AdS/CFT and Higher Spin Gravity
• Field Theory of Primaries in W_N Minimal Models
• Thermofield Duality for Higher Spin Rindler Gravity
• The Collective Field Theory of a Singular Supersymmetric Matrix Model

Cited by in corpus (34)

• Phase Diagram of Planar Matrix Quantum Mechanics, Tensor, and Sachdev-Ye-Kitaev Models
• Complete random matrix classification of SYK models with $\mathcal{N}=0$, $1$ and $2$ supersymmetry
• Space-Time in the SYK Model
• SYK Models and SYK-like Tensor Models with Global Symmetry
• Correlators in the $\mathcal{N}=2$ Supersymmetric SYK Model
• Three Dimensional View of Arbitrary $q$ SYK models
• Gauge Invariants, Correlators and Holography in Bosonic and Fermionic Tensor Models
• Thouless time for mass-deformed SYK
• SYK Model, Chaos and Conserved Charge
• Phases Of Melonic Quantum Mechanics
• Contrasting SYK-like Models
• Cut and join operator ring in Aristotelian tensor model
• Towards the Holographic Dual of N = 2 SYK
• A new class of SYK-like models with maximal chaos
• Supersymmetric SYK Model with Global Symmetry
• On thermalization in the SYK and supersymmetric SYK models
• From Kronecker to tableau pseudo-characters in tensor models
• Chaos and random matrices in supersymmetric SYK
• On Melonic Supertensor Models
• $T\overline{T}$ Deformations of Supersymmetric Quantum Mechanics
• Chiral Algebras of Two-Dimensional SYK Models
• Chaos in Three-dimensional Higher Spin Gravity
• Spontaneous Symmetry Breaking in Tensor Theories
• On 1D, N = 4 Supersymmetric SYK-Type Models (I)
• Quantum Correction to Chaos in Schwarzian Theory
• Models of phase stability in Jackiw-Teitelboim gravity
• Complete Solution of a Gauged Tensor Model
• SYK/AdS duality with Yang-Baxter deformations
• Supersymmetric Black Holes and the SJT/nSCFT${}_1$ Correspondence
• Extended supersymmetry with central charges in Dirac action with curved extra dimensions
• SYK Model with global symmetries in the double scaling limit
• Extended supersymmetry with central charges in higher dimensional Dirac action
• A route from maximal chaoticity to integrability
• Extended supersymmetry in Dirac action with extra dimensions