Supersymmetric Partially Massless Fields and Non-Unitary Superconformal Representations

TL;DR

This paper classifies supersymmetric multiplets in AdS4 containing partially massless fields by analyzing non-unitary superconformal representations, revealing new shortening conditions and providing explicit actions and transformations.

Contribution

It introduces a classification of ${ m extbf{N}=1}$ SUSY multiplets with partially massless fields in AdS4, including explicit actions and new shortening conditions for non-unitary representations.

Findings

Identified supermultiplets with partially massless spin-2 fields

Derived the AdS4 action and SUSY transformations for these multiplets

Discovered new shortening conditions for non-unitary superconformal representations

Abstract

We find and classify the ${\cal N}=1$ SUSY multiplets on AdS$_4$ which contain partially massless fields. We do this by studying the non-unitary representations of the $d=3$ superconformal algebra of the boundary. The simplest super-multiplet which contains a partially massless spin-2 particle also contains a massless photon, a massless spin-$3/2$ particle and a massive spin-$3/2$ particle. The gauge parameters form a Wess-Zumino super-multiplet which contains the gauge parameters of the photon, the partially massless graviton, and the massless spin-$3/2$ particle. We find the AdS$_4$ action and SUSY transformations for this multiplet. More generally, we classify new types of shortening conditions that can arise for non-unitary representations of the $d=3$ superconformal algebra.