Cubic interaction vertices for massless higher spin supermultiplets in d=4

TL;DR

This paper develops supersymmetric cubic interaction vertices for massless higher spin supermultiplets in four dimensions using a frame-like multispinor formalism, initially in AdS space and then in the flat limit.

Contribution

It introduces a uniform method for constructing supersymmetric cubic vertices for higher spin supermultiplets in 4D, utilizing the Fradkin-Vasiliev formalism and the multispinor approach.

Findings

Vertices constructed in AdS space are sums of four elementary components.

One of the elementary vertices vanishes in the flat limit, aligning with Metsaev's classification.

The formalism simplifies handling bosonic and fermionic fields uniformly.

Abstract

We construct a range of supersymmetric cubic vertices for three massless higher spin supermultiplets in the four-dimensional space. We use frame-like multispinor formalism, which allows to avoid most of the technical difficulties and provides a uniform description for bosons and fermions. Our work is based on the so-called Fradkin-Vasiliev formalism for construction of the cubic vertices, which requires the non-zero cosmological constant. Thus we first construct the vertices in AdS space and then consider the flat limit. We show that the AdS supersymmetric vertex is a sum of four elementary vertices for supermultiplet components, while one of the vertices vanishes in the flat limit in agreement with the Metsaev's classification.