Aspects of Weyl Supergravity

TL;DR

This paper analyzes the spectrum of conformal supergravities with various supersymmetries in four dimensions, revealing their unique ghost multiplet structures and discussing their holographic duals.

Contribution

It provides a detailed spectrum analysis of ${ m ext{Weyl}}$ supergravity theories for different ${ m ext{N}}$, including ghost multiplets and gauge symmetries, extending previous understanding.

Findings

Spectrum includes ghost graviton and gravitino multiplets.

Residual vector multiplet appears in non-maximal ${ m N}$ theories.

These theories likely lack standard 5D holographic duals.

Abstract

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