New locally (super)conformal gauge models in Bach-flat backgrounds

@article{Kuzenko2020NewL,
  title={New locally (super)conformal gauge models in Bach-flat backgrounds},
  author={Sergei M. Kuzenko and Michael Ponds and Emmanouil S. N. Raptakis},
  journal={arXiv: High Energy Physics - Theory},
  year={2020}
}
For every conformal gauge field $h_{\alpha (n)\dot \alpha (m)}$ in four dimensions, with $n\geq m >0$, a gauge-invariant action is known to exist in arbitrary conformally flat backgrounds. If the Weyl tensor is non-vanishing, however, gauge invariance holds for a pure conformal field in the following cases: (i) $n=m=1$ (Maxwell's field) on arbitrary gravitational backgrounds; and (ii) $n=m+1 =2 $ (conformal gravitino) and $n=m=2$ (conformal graviton) on Bach-flat backgrounds. It is believed… 

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