Symmetries of Holographic Super-Minimal Models

Abstract

We compute the asymptotic symmetry of the higher-spin supergravity theory in AdS_3 and obtain an infinite-dimensional non-linear superalgebra, which we call the super-W_infinity[lambda] algebra. According to the recently proposed supersymmetric duality between higher-spin supergravity in an AdS_3 background and the 't Hooft limit of the N=2 CP^n Kazama-Suzuki model on the boundary, this symmetry algebra should agree with the 't Hooft limit of the chiral algebra of the CFT, SW_n. We provide two nontrivial checks of the duality. By comparing the algebras, we explicitly match the lowest-spin commutation relations in the super-W_infinity[lambda] with the corresponding commutation relations in the 't Hooft limit on the CFT side. We also consider the degenerate representations of the two algebras and find that the spectra of the chiral primary fields are identical.

33 pages, references added, some errors corrected, discussions about the truncation of the shs[lambda] algebra and reobtaining the original shs[lambda] algebra from the super-W_infinity[lambda] algebra added

References in corpus (14)

• Asymptotic symmetries of three-dimensional gravity coupled to higher-spin fields
• Nonlinear W(infinity) Algebra as Asymptotic Symmetry of Three-Dimensional Higher Spin Anti-de Sitter Gravity
• Symmetries of Holographic Minimal Models
• Asymptotic W-symmetries in three-dimensional higher-spin gauge theories
• Spacetime Geometry in Higher Spin Gravity
• Higher Spin Black Holes from CFT
• Partition Functions of Holographic Minimal Models
• Higher spin AdS_3 supergravity and its dual CFT
• Higher Spin Gravity with Matter in AdS_3 and Its CFT Dual
• The Large N 't Hooft Limit of Coset Minimal Models
• Super-W(infinity) Asymptotic Symmetry of Higher-Spin AdS(3) Supergravity
• Scalar fields and three-point functions in D=3 higher spin gravity
• Correlation Functions in Holographic Minimal Models
• Minimal Model Holography for SO(2N)

Cited by in corpus (30)

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• Extended supersymmetry in AdS_3 higher spin theories
• Conical defects and N=2 higher spin holography
• $\mathcal{N}=(0,2)$ SYK, Chaos and Higher-Spins
• The $\mathcal{N}=1$ algebra ${\mathcal{W}}_{\infty }[\mu ]$ and its truncations
• Rectangular W-(super)algebras and their representations
• The Continuous Orbifold of N=2 Minimal Model Holography
• Superconformal blocks from Wilson lines with loop corrections
• Higher Spin Currents in the N=2 Stringy Coset Minimal Model
• On the partition functions of higher spin black holes
• Higher Spin Currents in Wolf Space for Generic N
• Higher Spin Currents in Orthogonal Wolf Space
• Rectangular W-algebras of types $so(M)$ and $sp(2M)$ and dual coset CFTs
• Exploring new Boundary Conditions for $\mathcal{N}=(1,1)$ Extended Higher Spin $Ad{S}_3$ Supergravity
• Higher-spin gauge theories in three spacetime dimensions
• Higher-spin charges in Hamiltonian form. II. Fermi fields
• The $\mathcal{N}=4$ Coset Model and the Higher Spin Algebra
• The $\mathcal{N}=4$ Higher Spin Algebra for Generic $\mu$ Parameter
• The $\mathcal{N}=2$ Supersymmetric $w_{1+\infty }$ Symmetry in the Two-Dimensional SYK Models
• Higher Spin Currents in the Enhanced N=3 Kazama-Suzuki Model
• $\mathcal{N}=(2,2)$ extended $\mathfrak{sl}(3|2)$ Chern-Simons $Ad{S}_3$ supergravity with new boundaries
• A Supersymmetric Enhancement of $\mathcal{N}=1$ Holographic Minimal Model
• Adding Complex Fermions to the Grassmannian-like Coset Model
• Higher Spin Currents with Manifest $SO(4)$ Symmetry in the Large $\mathcal{N}=4$ Holography
• The Grassmannian-like Coset Model and the Higher Spin Currents
• Super Virasoro Algebras From Chiral Supergravity