Aspects of Weyl Supergravity

Abstract

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.

23 pages, Replaced version agrees with published version in JHEP

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• On the Vacuum Structure of the $\mathcal{N}=4$ Conformal Supergravity