Extended supersymmetry in AdS_3 higher spin theories

Abstract

We determine the asymptotic symmetry algebra (for fields of low spin) of the $M\times M$ matrix extended Vasiliev theories on AdS${}_3$ and find that it agrees with the $\mathcal{W}$-algebra of their proposed coset duals. Previously it was noticed that for $M=2$ the supersymmetry increases from $\mathcal{N}=2$ to $\mathcal{N}=4$. We study more systematically this type of supersymmetry enhancements and find that, although the higher spin algebra has extended supersymmetry for all $M\ge 2$, the corresponding asymptotic symmetry algebra fails to be superconformal except for $M=2$, when it has large $\mathcal{N}=4$ superconformal symmetry. Moreover, we find that the Vasiliev theories based on $sh{s}^E\left(\mathcal{N}|2,\mathbb{R}\right)$ are special cases of the matrix extended higher spin theories, and hence have the same supersymmetry properties.

arXiv comment23 pages

References in corpus (32)

• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• AdS Dual of the Critical O(N) Vector Model
• Fractional M2-branes
• 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
• An AdS_3 Dual for Minimal Model CFTs
• Chern-Simons Theory with Vector Fermion Matter
• Microscopic Formulation of Black Holes in String Theory
• Higher-Spin Gauge Interactions for Massive Matter Fields in 3D AdS Space-Time
• Measurement of $J/\psi$ helicity distributions in inelastic photoproduction at HERA
• Minimal Model Holography
• d=3 Bosonic Vector Models Coupled to Chern-Simons Gauge Theories
• Symmetries of Holographic Minimal Models
• Higher Spins & Strings
• One Loop Tests of Higher Spin AdS/CFT
• Asymptotic Dynamics and Asymptotic Symmetries of Three-Dimensional Extended AdS Supergravity
• Large N=4 Holography
• Super-W(infinity) Asymptotic Symmetry of Higher-Spin AdS(3) Supergravity
• Extended higher spin holography and Grassmannian models
• Higher spin AdS_3 holography with extended supersymmetry
• The symmetry of large N=4 holography
• 3D Higher-Spin Gauge Theories with Matter
• N=1 extension of minimal model holography
• Symmetries of Holographic Super-Minimal Models
• On the coset duals of extended higher spin theories
• Higher Spin Currents in Wolf Space: Part I
• The $\mathcal{N}=1$ algebra ${\mathcal{W}}_{\infty }[\mu ]$ and its truncations
• The Continuous Orbifold of N=2 Minimal Model Holography
• Symmetries and symmetry-breaking in string theory
• The large $\mathcal{N}=4$ superconformal ${\mathcal{W}}_{\infty }$ algebra
• Higher Spin Currents in Wolf Space: Part II
• Aspects of Higher-Spin Theory with Fermions

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• Stringy $\mathcal{N}=(2,2)$ holography for AdS${}_3$
• Higher spins in the symmetric orbifold of K3
• Higher spin algebras and large $\mathcal{N}=4$ holography
• Higher Spins in Hyper-Superspace
• Higher Spin Currents in Orthogonal Wolf Space
• Rectangular W-algebras of types $so(M)$ and $sp(2M)$ and dual coset CFTs
• Higher-spin gauge theories in three spacetime dimensions
• Higher Spin Currents in the Enhanced N=3 Kazama-Suzuki Model
• Higher-spin charges in Hamiltonian form. II. Fermi fields
• Higgs phenomenon for higher spin fields on AdS_3
• Asymptotic Symmetries of Colored Gravity in Three Dimensions
• Even spin $\mathcal{N}=4$ holography
• Marginal deformations and the Higgs phenomenon in higher spin AdS_3 holography
• Supersymmetric Localization in AdS${}_5$ and the Protected Chiral Algebra
• Chiral Ring of Strange Metals: The Multicolor Limit
• Higher spin holography with Galilean symmetry in general dimensions