On massive higher spin supermultiplets in d=3

TL;DR

This paper develops a gauge-invariant framework for constructing off-shell cubic vertices involving massive higher spin supermultiplets in three dimensions, ensuring supersymmetry and gauge invariance.

Contribution

It introduces a new method for constructing off-shell cubic vertices for massive higher spin supermultiplets in d=3, maintaining supersymmetry and gauge invariance.

Findings

Constructed off-shell cubic vertices for supermultiplets.

Ensured invariance under local supersymmetry transformations.

Validated the approach with lower superspin examples.

Abstract

In this paper, using a frame-like gauge invariant formulation of the massive higher spin bosons and fermions, we develop a direct construction of the completely off-shell cubic vertices describing an interaction of the massless gravitino with the massive higher spin supermultiplets. To achieve the invariance under the local supersymmetry we introduce all necessary supertransformations (both for the physical as well as for the auxiliary fields) and thus all the supercurrents constructed are conserved on-shell. As an illustration of the technique used we present some lower superspin examples and then we consider the arbitrary superspin. We also check that the whole construction is completely consistent with all bosonic and fermionic gauge symmetries of the fields entering the supermultiplets.