N=2 AdS supergravity and supercurrents

Abstract

We consider the minimal off-shell formulation for four-dimensional N=2 supergravity with a cosmological term, in which the second compensator is an improved tensor multiplet. We use it to derive a linearized supergravity action (and its dual versions) around the anti-de Sitter (AdS) background in terms of three N=2 off-shell multiplets: an unconstrained scalar superfield, vector and tensor multiplets. This allows us to deduce the structure of the supercurrent multiplet associated with those supersymmetric theories which naturally couple to the supergravity formulation chosen, with or without a cosmological term. Finally, our linearized N=2 AdS supergravity action is reduced to N=1 superspace. The result is a sum of two N=1 linearized actions describing (i) old minimal supergravity; and (ii) an off-shell massless gravitino multiplet. We also derive dual formulations for the massless N=1 gravitino multiplet in AdS. As a by-product of our consideration, we derive the consistent supergravity extension of the N=1 supercurrent multiplet advocated recently by Komargodski and Seiberg.

53 pages; v2. typos corrected, references added

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• The structure of N=2 supersymmetric nonlinear sigma models in AdS_4
• Symmetries of curved superspace in five dimensions
• Superconformal duality-invariant models and $\mathcal{N}=4$ SYM effective action
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• Extended superconformal higher-spin gauge theories in four dimensions
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• New Fayet-Iliopoulos terms in $\mathcal{N}=2$ supergravity
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• On higher-spin $\mathcal{N}=2$ supercurrent multiplets
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• Vector-tensor supermultiplets in AdS and supergravity
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• Off-shell invariants of linearized $4D,\mathcal{N}=2$ supergravity in the harmonic approach
• $\mathcal{N}=2$ AdS hypermultiplets in harmonic superspace
• Topics in 3D N=2 AdS supergravity in superspace
• The conformal supercurrents in diverse dimensions and conserved superconformal currents