Abstract
In this article we study the higher-spin algebra behind the type-A cubic couplings recently extracted from the free O(N ) model in generic dimensions, demonstrating that they coincide with the known structure constants for the unique higher-spin algebra in generic dimensions. This provides an explicit check of the holographic reconstruction and of the duality between higher-spin theories and the free O(N ) model in generic dimensions, generalising the result of Giombi and Yin in AdS4. For completeness, we also address the same problem in the flat space for the cubic couplings derived by Metsaev in 1991, which are recovered from the flat limit of the AdS type-A cubic couplings. We observe that both flat and AdS4 higher-spin Lorentz subalgebras coincide, hinting towards the existence of a full higher-spin symmetry behind the flat-space cubic couplings of Metsaev.
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Sleight, C., Taronna, M. Higher-spin algebras, holography and flat space. J. High Energ. Phys. 2017, 95 (2017). https://doi.org/10.1007/JHEP02(2017)095
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DOI: https://doi.org/10.1007/JHEP02(2017)095