Field theories with (2,0) AdS supersymmetry in $\mathcal{N}=1$ AdS superspace

Abstract

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 realised 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 $\hat{s}$, integer $(\hat{s}=s)$ or half-integer $(\hat{s}=s+1/2)$, with $s=1,2,\dots$, we obtain two off-shell formulations for a massless $\mathcal{N}=1$ superspin-$\hat{s}$ multiplet in 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 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 AdS${}_3$.

55 pages; V2: comments and references added

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Cited by in corpus (4)

• Cubic Vertices for N=1 Supersymmetric Massless Higher Spin Fields in Various Dimensions
• Cubic interactions of arbitrary spin fields in 3d flat space
• Super Non-Abelian T-Duality
• Higher-spin gauge models with (1,1) supersymmetry in AdS${}_3$: Reduction to (1,0) superspace