Extended superconformal higher-spin gauge theories in four dimensions

Abstract

Using the off-shell formulation for $\mathcal{N}=2$ conformal supergravity in four dimensions, we describe superconformal higher-spin multiplets of conserved currents in a curved background and present their associated unconstrained gauge prepotentials. The latter are used to construct locally superconformal chiral actions, which are demonstrated to be gauge invariant in arbitrary conformally flat backgrounds. The main $\mathcal{N}=2$ results are then generalised to the $\mathcal{N}$-extended case. We also present the gauge-invariant field strengths for on-shell massless higher-spin $\mathcal{N}=2$ supermultiplets in anti-de Sitter space. These field strengths prove to furnish representations of the $\mathcal{N}=2$ superconformal group.

31 pages; V3: title changed, references and comments added, a new section included, accepted for publication in JHEP

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• $\mathcal{N}=2$ superconformal higher-spin multiplets and their hypermultiplet couplings
• On higher-spin $\mathcal{N}=2$ supercurrent multiplets
• The anti-de Sitter supergeometry revisited
• Three-point functions of conserved currents in 4D CFT: general formalism for arbitrary spins
• $\mathcal{N}=2$ superconformal gravitino in harmonic superspace
• Self-duality for $\mathcal{N}$-extended superconformal gauge multiplets
• $\mathcal{N}=2$ higher-spin supercurrents
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• Supersymmetry at BLTP: Recent Progress in Two Directions