Abstract
The problem of constructing gauge-invariant actions for conformal higher-spin fields in curved backgrounds is known to be notoriously difficult. In this paper we present gauge-invariant models for conformal maximal depth fields with spin s = 5/2 and s = 3 in four-dimensional Bach-flat backgrounds. We find that certain lower-spin fields must be introduced to ensure gauge invariance when s > 2, which is analogous to a conjecture made earlier in the literature for conformal higher-spin fields of minimal depth.
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Kuzenko, S.M., Ponds, M. Generalised conformal higher-spin fields in curved backgrounds. J. High Energ. Phys. 2020, 21 (2020). https://doi.org/10.1007/JHEP04(2020)021
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DOI: https://doi.org/10.1007/JHEP04(2020)021