Aspects of Weyl supergravity

Abstract

Abstract In this paper we study the spectrum of all conformal, $$ \mathcal{N} $$ N -extended supergravities ( $$ \mathcal{N} $$ N = 1, 2, 3, 4) in four space-time dimensions. When these theories are obtained as massless limit of Einstein plus Weyl2 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 $$ \mathcal{N} $$ N -fold tripole ghost gravitino, the third state belonging to a spin 3/2 multiplet and a residual vector multiplet present for non-maximal $$ \mathcal{N} $$ N < 4 theories. These theories are not expected to have a standard gravity holographic dual in five dimensions.