Chiral Algebras of Two-Dimensional SYK Models

Abstract

We study chiral algebras in the $\bar{Q}$-cohomology of two dimensional SYK models with extended supersymmetry. In a special limit discovered in arXiv:1805.09325, we are able to construct explicitly a "vertical" single-particle higher-spin algebra that is bilinear in the fundamental fields. This algebra can be regarded as the counterpart, when going away from criticality, of the infrared emergent higher-spin symmetry of the $\mathcal{N}=(0,2)$ SYK model. Moreover, a second "horizontal" single-particle higher-spin algebra appears in this limit. Together with the vertical algebra they generate a stringy algebra with a "higher spin square" structure that is believed to appear in the tensionless limit of string theory. On the other hand, we do not find single-particle higher-spin algebra away from the special limit, which is consistent with the result in arXiv:1805.09325. Our analysis is carried out for each individual realization of the random couplings and for finite $N$ (and $M$), which in particular indicates that the conclusion in arXiv:1805.09325 is robust to $1/N$ corrections.

arXiv comment25 pages

References in corpus (68)

• A bound on chaos
• Gapless Spin-Fluid Ground State in a Random Quantum Heisenberg Magnet
• Comments on the Sachdev-Ye-Kitaev model
• Phases of $N=2$ Theories In Two Dimensions
• Black holes and the butterfly effect
• Chaos in AdS${}_2$ holography
• The Spectrum in the Sachdev-Ye-Kitaev Model
• An Investigation of AdS${}_2$ Backreaction and Holography
• W-symmetry in Conformal Field Theory
• Anti-de Sitter Fragmentation
• The soft mode in the Sachdev-Ye-Kitaev model and its gravity dual
• 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
• A Generalization of Sachdev-Ye-Kitaev
• Sachdev-Ye-Kitaev Model as Liouville Quantum Mechanics
• Stringy gravity, interacting tensionless strings and massless higher spins
• Solving the Schwarzian via the Conformal Bootstrap
• AdS2 Quantum Gravity and String Theory
• Non-Fermi liquid regime of a doped Mott insulator
• Triality in Minimal Model Holography
• Bi-Local Holography in the SYK Model
• Higher Spins & Strings
• Power-law out of time order correlation functions in the SYK model
• Operator growth in the SYK model
• More on Supersymmetric and 2d Analogs of the SYK Model
• The Quantum Gravity Dynamics of Near Extremal Black Holes
• Overscreened multi-channel SU(N) Kondo model : large-N solution and Conformal Field Theory
• On the Landau-Ginzburg Description of $N=2$ Minimal Models
• The Bulk Dual of SYK: Cubic Couplings
• Bounding the Space of Holographic CFTs with Chaos
• All point correlation functions in SYK
• The affine Yangian of ${\mathfrak{gl}}_1$ revisited
• Statistical mechanics of a two-dimensional black hole
• W-symmetry, topological vertex and affine Yangian
• Towards a 2d QFT Analog of the SYK Model
• A Supersymmetric SYK-like Tensor Model
• Instability of the non-Fermi liquid state of the Sachdev-Ye-Kitaev Model
• Elliptic Genera and N=2 Superconformal Field Theory
• Coset Realization of Unifying W-Algebras
• Quantum continuous ${\mathfrak{gl}}_{\infty }$: Semi-infinite construction of representations
• ABJ Triality: from Higher Spin Fields to Strings
• Menagerie of AdS${}_2$ boundary conditions
• On the relation between the magnitude and exponent of OTOCs
• Tunable Quantum Chaos in the Sachdev-Ye-Kitaev Model Coupled to a Thermal Bath
• String Theory as a Higher Spin Theory
• Computing the Complete Massless Spectrum of a Landau-Ginzburg Orbifold
• Duality in N=2 minimal model holography
• Space-Time in the SYK Model
• Global U(1) R-Symmetry And Conformal Invariance Of (0,2) Models
• Geometry of (0,2) Landau-Ginzburg Orbifolds
• A line of CFTs: from generalized free fields to SYK
• Correlators in the $\mathcal{N}=2$ Supersymmetric SYK Model
• Three Dimensional View of Arbitrary $q$ SYK models
• Does the SYK model have a spin glass phase?
• Higher Spins and Yangian Symmetries
• Vector models and generalized SYK models
• Supersymmetric SYK Model: Bi-local Collective Superfield/Supermatrix Formulation
• From Coxeter Higher-Spin Theories to Strings and Tensor Models
• Comments on the Random Thirring Model
• Boundary theories for dilaton supergravity in 2D
• The supersymmetric affine Yangian
• $\mathcal{N}=2$ SYK model in the superspace formalism
• Twin-plane-partitions and $\mathcal{N}=2$ affine Yangian
• $\mathcal{N}=(0,2)$ SYK, Chaos and Higher-Spins
• On Melonic Supertensor Models
• Classification of Structure Constants for W-algebras from Highest Weights
• Twisted sectors from plane partitions

Cited by in corpus (11)

• A 3d disordered superconformal fixed point
• Soft modes in $\mathcal{N}=2$ SYK model
• The $\mathcal{N}=2$ Supersymmetric $w_{1+\infty }$ Symmetry in the Two-Dimensional SYK Models
• The $\mathcal{N}=4$ Coset Model and the Higher Spin Algebra
• The $\mathcal{N}=4$ Higher Spin Algebra for Generic $\mu$ Parameter
• Chiral Sachdev-Ye model: Integrability and chaos of anyons in 1+1d
• Supersymmetric Landau-Ginzburg Tensor Models
• Ensemble averages, Poisson processes and Microstates
• The Grassmannian-like Coset Model and the Higher Spin Currents
• Gauging the complex SYK model
• Off-diagonal coupling of supersymmetric SYK model