In three dimensions, it is known that field theories possessing extended $(p,q)$ anti-de Sitter (AdS) supersymmetry with $\mathcal{N}=p+q\ge 3$ can be realized in (2,0) AdS superspace. Here we present a formalism to reduce every field theory with (2,0) AdS supersymmetry to $\mathcal{N}=1$ AdS superspace. As nontrivial examples, we consider supersymmetric nonlinear sigma models formulated in terms of $\mathcal{N}=2$ chiral and linear supermultiplets. The $(2,0)\to (1,0)$ AdS reduction technique is then applied to the off-shell massless higher-spin supermultiplets in (2,0) AdS superspace constructed in [1]. As a result, for each superspin value $\widehat{s}$, integer $(\widehat{s}=s)$ or half-integer $(\widehat{s}=s+\frac{1}{2})$, with $s=1,2,\dots$, we obtain two off-shell formulations for a massless $\mathcal{N}=1$ $\mathrm{superspin}\text{−}\widehat{s}$ multiplet in ${\mathrm{AdS}}_3$. These models prove to be related to each other by a superfield Legendre transformation in the flat superspace limit, but the duality is not lifted to the AdS case. Two out of the four series of $\mathcal{N}=1$ supersymmetric higher-spin models thus derived are new. The constructed massless $\mathcal{N}=1$ supersymmetric higher-spin actions in ${\mathrm{AdS}}_3$ are used to formulate (i) higher-spin supercurrent multiplets in $\mathcal{N}=1$ AdS superspace, and (ii) new topologically massive higher-spin off-shell supermultiplets. Examples of $\mathcal{N}=1$ higher-spin supercurrents are given for models of a complex scalar supermultiplet. We also present two new off-shell formulations for a massive $\mathcal{N}=1$ gravitino supermultiplet in ${\mathrm{AdS}}_3$.

• Received 11 June 2019

DOI:https://doi.org/10.1103/PhysRevD.100.045010

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Published by the American Physical Society