Abstract
The off-shell actions for \( \mathcal{N} \) -extended conformal supergravity theories in three dimensions were formulated in [1, 2] for 1 ≤ \( \mathcal{N} \) ≤ 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 super-multiplets in \( \mathcal{N} \) -extended supersymmetry. Our analysis leads to general expressions for identically conserved higher-spin current multiplets in \( \mathcal{N} \) -extended supersymmetry.
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Buchbinde, E.I., Hutchings, D., Hutomo, J. et al. Linearised actions for \( \mathcal{N} \) -extended (higher-spin) superconformal gravity. J. High Energ. Phys. 2019, 77 (2019). https://doi.org/10.1007/JHEP08(2019)077
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DOI: https://doi.org/10.1007/JHEP08(2019)077