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

References in corpus (4)

• Gauge invariant formulation of massive totally symmetric fermionic fields in (A)dS space
• Off-shell massive N=1 supermultiplets in three dimensions
• Off-shell superconformal nonlinear sigma-models in three dimensions
• Frame-like gauge invariant Lagrangian formulation of massive fermionic higher spin fields in AdS_3 space