A Fedosov-quantized Wigner function and the Feigin-Felder-Shoikhet trace yield a manifestly covariant action for scalar matter coupled to conformal higher-spin backgrounds.
Generalised conformal higher-spin fields in curved backgrounds
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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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Scalar Field on a higher-spin Background via Fedosov quantization
A Fedosov-quantized Wigner function and the Feigin-Felder-Shoikhet trace yield a manifestly covariant action for scalar matter coupled to conformal higher-spin backgrounds.