$ \mathcal{N} = 2 $ AdS supergravity and supercurrents

Abstract

We consider the minimal off-shell formulation for four-dimensional \( \mathcal{N} = 2 \) supergravity with a cosmological term, in which the second compensator is an improved tensormultiplet. We use it to derive a linearized supergravity action (and its dual versions) around the anti-de Sitter (AdS) background in terms of three \( \mathcal{N} = 2 \) 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 \( \mathcal{N} = 2 \) AdS supergravity action is reduced to \( \mathcal{N} = 1 \) superspace. The result is a sum of two \( \mathcal{N} = 1 \) linearized actions describing (i) old minimal supergravity; and (ii) an off-shell massless gravitino multiplet. We also derive dual formulations for the massless \( \mathcal{N} = 1 \) gravitino multiplet in AdS. As a by-product of our consideration, we derive the consistent supergravity extension of the \( \mathcal{N} = 1 \) supercurrent multiplet advocated recently by Komargodski and Seiberg.