Abstract
We propose generalised \( \mathcal{N} \) = 1 superconformal higher-spin (SCHS) gauge multiplets of depth t, \( {\Upsilon}_{\alpha (n)\overset{\cdot }{\alpha }(m)}^{(t)} \), with n ≥ m ≥ 1. At the component level, for t > 2 they contain generalised conformal higher-spin (CHS) gauge fields with depths t − 1, t and t + 1. The supermultiplets with t = 1 and t = 2 include both ordinary and generalised CHS gauge fields. Super-Weyl and gauge invariant actions describing the dynamics of \( {\Upsilon}_{\alpha (n)\overset{\cdot }{\alpha }(m)}^{(t)} \) on conformally-flat superspace backgrounds are then derived. For the case n = m = t = 1, corresponding to the maximal-depth conformal graviton supermultiplet, we extend this action to Bach-flat backgrounds. Models for superconformal non-gauge multiplets, which are expected to play an important role in the Bach-flat completions of the models for \( {\Upsilon}_{\alpha (n)\overset{\cdot }{\alpha }(m)}^{(t)} \), are also provided. Finally we show that, on Bach-flat backgrounds, requiring gauge and Weyl invariance does not always determine a model for a CHS field uniquely.
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Kuzenko, S.M., Ponds, M. & Raptakis, E.S.N. Generalised superconformal higher-spin multiplets. J. High Energ. Phys. 2021, 183 (2021). https://doi.org/10.1007/JHEP03(2021)183
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DOI: https://doi.org/10.1007/JHEP03(2021)183