In three dimensions, there are two types of $\mathcal{N}=2$ anti–de Sitter (AdS) supersymmetry, which are denoted (1, 1) and (2, 0). They are characterized by different supercurrents and support different families of higher-spin gauge models (massless and massive), which were constructed in Hutomo et al. [$\mathcal{N}=2$ supersymmetric higher spin gauge theories and current multiplets in three dimensions, Phys. Rev. D 98, 125004 (2018); Higher spin supermultiplets in three dimensions: (2, 0) AdS supersymmetry, Phys. Lett. B 787, 175 (2018)] for the (1, 1) and (2, 0) cases, respectively, using superspace techniques. It turns out that the precise difference between the (1, 1) and (2, 0) higher-spin supermultiplets can be pinned down by reducing these gauge theories to (1, 0) AdS superspace. The present paper is devoted to the $(1,1)\to (1,0)$ AdS superspace reduction. In conjunction with the outcomes of the $(2,0)\to (1,0)$ AdS superspace reduction carried out in Hutomo and Kuzenko [Field theories with (2, 0) AdS supersymmetry in $\mathcal{N}=1$ AdS superspace, Phys. Rev. D 100, 045010 (2019)], we demonstrate that every known higher-spin theory with (1, 1) or (2, 0) AdS supersymmetry decomposes into a sum of two off-shell (1, 0) supermultiplets that belong to four series of inequivalent higher-spin gauge models. The latter are reduced to components.

• Received 15 December 2020
• Accepted 3 May 2021

DOI:https://doi.org/10.1103/PhysRevD.103.126023

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Published by the American Physical Society