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.

23 pages

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Cited by in corpus (6)

• Higher Spins in Hyper-Superspace
• Higher Spin Currents in Orthogonal Wolf Space
• Higher-spin gauge theories in three spacetime dimensions
• Higher-spin charges in Hamiltonian form. II. Fermi fields
• Higher Spin Currents in the Enhanced N=3 Kazama-Suzuki Model
• Supersymmetric Localization in AdS${}_5$ and the Protected Chiral Algebra