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Higher-spin algebras, holography and flat space. (English) Zbl 1377.83008

Summary: 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 doi:10.1007/JHEP09(2010)115 in \(AdS_{4}\). For completeness, we also address the same problem in the flat space for the cubic couplings derived by Metsaev [R. R. Metsaev, Mod. Phys. Lett. A 6, No. 4, 359–367 (1991; Zbl 1021.81542)], [R. R. Metsaev, Mod. Phys. Lett. A 6, No. 26, 2411–2421 (1991; Zbl 1020.81941)] in 1991, which are recovered from the flat limit of the AdS type-A cubic couplings. We observe that both flat and \(AdS_{4}\) higher-spin Lorentz subalgebras coincide, hinting towards the existence of a full higher-spin symmetry behind the flat-space cubic couplings of Metsaev.

MSC:

83C05 Einstein’s equations (general structure, canonical formalism, Cauchy problems)
83D05 Relativistic gravitational theories other than Einstein’s, including asymmetric field theories
81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics
81R25 Spinor and twistor methods applied to problems in quantum theory
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