A note on partially massless supergravity

TL;DR

This paper investigates the interactions of partially massless spin-2 fields with spin-3/2 fields, revealing obstructions to gauge algebra closure and proposing a consistent theory involving conformal supergravity in AdS4.

Contribution

It classifies all parity-invariant deformations of the free theory and shows that consistent coupling requires adding a massless graviton, leading to a new perspective on supergravity theories.

Findings

Re-derivation of a non-Abelian vertex similar to previous work

Identification of obstructions to gauge algebra closure at next order

Proposal of a consistent theory involving conformal supergravity

Abstract

We analyse the couplings of a partially massless spin-2 field with a doublet of massless, real spin-3/2 fields. In the flat limit, this spectrum coincides with the spectrum of ${\cal N}=2$ pure supergravity around anti-de Sitter spacetime AdS$_4$. We classify all the possible parity-invariant, non-Abelian deformations of the free theory that lead to a deformation of the Lagrangian. By doing this, we re-derive a non-Abelian vertex recently found in 2412.04982 [hep-th] by Yu. M. Zinoviev following a different approach, and show that the corresponding non-Abelian gauge algebra closely resembles the one of ${\cal N}=2$ supergravity around AdS$_4$. The gauge-algebra deformation is however obstructed, at next order. Then, we add a massless vector field together with a massive spin-3/2 field, and find two nontrivial vertices mixing these fields with a single massless gravitino. Still, the gauge algebra remains obstructed at next order, therefore excluding the possibility to make local the global supersymmetry algebra found in recent works on partially massless supermultiplets in AdS$_4$. Finally, we argue that the two problems encountered are simultaneously solved by the addition of the masseless graviton, leading to ${\cal N}=1$ pure conformal supergravity around AdS$_4$ as the only consistent theory coupling partially massless spin-2 fields to massless and massive spin-3/2 fields.