Aspects of Weyl Supergravity

In this paper we study the spectrum of all conformal, $ \mathcal{N} $ -extended supergravities ( $ \mathcal{N} $ = 1, 2, 3, 4) in four space-time dimensions. When these theories are obtained as massless limit of Einstein plus Weyl$^{2}$ supergravity, the appropriate counting of the enhanced gauge symmetries allow us to derive the massless spectrum which consist of a dipole ghost graviton multiplet, a $ \mathcal{N} $ -fold tripole ghost gravitino, the third state belonging to a spin 3/2 multiplet and a residual vector multiplet present for non-maximal $ \mathcal{N} $ < 4 theories. These theories are not expected to have a standard gravity holographic dual in five dimensions.