Abstract
We determine the asymptotic symmetry algebra (for fields of low spin) of the M × M matrix extended Vasiliev theories on AdS3 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 ≥ 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 \( \mathfrak{s}\mathfrak{h}{\mathfrak{s}}^E\left(\mathcal{N}\Big|2,\mathrm{\mathbb{R}}\right) \) are special cases of the matrix extended higher spin theories, and hence have the same supersymmetry properties.
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Candu, C., Peng, C. & Vollenweider, C. Extended supersymmetry in AdS3 higher spin theories. J. High Energ. Phys. 2014, 113 (2014). https://doi.org/10.1007/JHEP12(2014)113
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DOI: https://doi.org/10.1007/JHEP12(2014)113