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

DOI10.1007/JHEP08(2019)077zbMATH Open1421.83130arXiv1905.12476OpenAlexW2998316378MaRDI QIDQ2273429

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Publication date: 23 September 2019

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Abstract: The off-shell actions for $calN$-extended conformal supergravity theories in three dimensions were formulated in [1,2] for $1leqcalNleq6$ using a universal approach. Each action is generated by a closed super three-form which is constructed in terms of the constrained geometry of $calN$-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 $calN$-extended Minkowski superspace and then use them to construct linearised rank-$n$ super-Cotton tensors and off-shell $calN$-extended superconformal actions. We also propose off-shell gauge-invariant actions to describe massive higher-spin supermultiplets in $calN$-extended supersymmetry. Our analysis leads to general expressions for identically conserved higher-spin current multiplets in $calN$-extended supersymmetry.

Full work available at URL: https://arxiv.org/abs/1905.12476

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