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arXiv · 1905.12476

Linearised actions for $\cal N$-extended (higher-spin) superconformal gravity

Evgeny I. Buchbinder·Daniel Hutchings·Jessica Hutomo·Sergei M. Kuzenko
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Abstract

The off-shell actions for $\cal N$-extended conformal supergravity theories in three dimensions were formulated in [1,2] for $1\leq {\cal N} \leq 6$ using a universal approach. Each action is generated by a closed super three-form which is constructed in terms of the constrained geometry of $\cal N$-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 $\cal N$-extended Minkowski superspace and then use them to construct linearised rank-$n$ super-Cotton tensors and off-shell $\cal N$-extended superconformal actions. We also propose off-shell gauge-invariant actions to describe massive higher-spin supermultiplets in $\cal N$-extended supersymmetry. Our analysis leads to general expressions for identically conserved higher-spin current multiplets in $\cal N$-extended supersymmetry.

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Evgeny I. Buchbinder, Daniel Hutchings, Jessica Hutomo, Sergei M. Kuzenko. 2019-05-29. Linearised actions for $\cal N$-extended (higher-spin) superconformal gravity. https://arxiv.org/abs/1905.12476

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