${\cal N}=2$ Supersymmetric Partially Massless Fields and Non-Unitary Superconformal Representations

TL;DR

This paper classifies ${ m N}=2$ supersymmetric multiplets in AdS$_4$ that include partially massless fields, revealing new short multiplets and exotic field content, and explores their boundary superconformal representations.

Contribution

It introduces a classification of ${ m N}=2$ supermultiplets with partially massless fields, including new shortening conditions and exotic field content not seen in ${ m N}=1$ cases.

Findings

Short ${ m N}=2$ multiplet containing a partially massless spin-2 field.

Existence of exotic fields within these multiplets.

${ m N}=2$ supersymmetry allows for short multiplets with partially massless particles of various spins.

Abstract

We find and classify the simplest ${\cal N}=2$ SUSY multiplets on AdS$_4$ which contain partially massless fields. We do this by studying representations of the ${\cal N}=2$, $d=3$ superconformal algebra of the boundary, including new shortening conditions that arise in the non-unitary regime. Unlike the ${\cal N}=1$ case, the simplest ${\cal N}=2$ multiplet containing a partially massless spin-2 is short, containing several exotic fields. More generally, we argue that ${\cal N}=2$ supersymmetry allows for short multiplets that contain partially massless spin-$s$ particles of depth $t=s-2$.