Linearised actions for $\mathcal{N}$-extended (higher-spin) superconformal gravity

Abstract

The off-shell actions for $\mathcal{N}$-extended conformal supergravity theories in three dimensions were formulated in [1,2] for $1\le \mathcal{N}\le 6$ using a universal approach. Each action is generated by a closed super three-form which is constructed in terms of the constrained geometry of $\mathcal{N}$-extended conformal superspace. In this paper we initiate a program to recast these actions (and to formulate their higher-spin counterparts) in terms of unconstrained gauge prepotentials as integrals over the full superspace. We derive transverse projection operators in $\mathcal{N}$-extended Minkowski superspace and then use them to construct linearised rank-$n$ super-Cotton tensors and off-shell $\mathcal{N}$-extended superconformal actions. We also propose off-shell gauge-invariant actions to describe massive higher-spin supermultiplets in $\mathcal{N}$-extended supersymmetry. Our analysis leads to general expressions for identically conserved higher-spin current multiplets in $\mathcal{N}$-extended supersymmetry.

30 pages; V2: Comments and references added, typos corrected

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• Unconstrained off-shell superfield formulation of $4D,\mathcal{N}=2$ supersymmetric higher spins
• Extended superconformal higher-spin gauge theories in four dimensions
• Spin projection operators in (A)dS and partial masslessness
• AdS superprojectors
• The renormalization structure of $6D$, $\mathcal{N}=(1,0)$ supersymmetric higher-derivative gauge theory
• Higher-spin gauge models with (1,1) supersymmetry in AdS${}_3$: Reduction to (1,0) superspace
• AdS (super)projectors in three dimensions and partial masslessness