Progress on cubic interactions of arbitrary superspin supermultiplets via gauge invariant supercurrents

TL;DR

This paper explores cubic interactions involving superspin supermultiplets, identifying two types of gauge-invariant supercurrents that enable consistent non-minimal interactions for various superspin values.

Contribution

It introduces two classes of gauge-invariant supercurrents for superspin interactions, expanding understanding of non-minimal cubic couplings in supersymmetric theories.

Findings

Conformal superspin supercurrents exist only for even s, s=2ℓ+2, and are unique.

Poincaré superspin supercurrents exist for all s and Y values.

Two types of consistent supercurrents are identified for cubic interactions.

Abstract

We consider cubic interactions of the form $s-Y-Y$ between a massless integer superspin $s$ supermultiplet and two massless arbitrary integer or half integer superspin $Y$ supermultiplets. We focus on non-minimal interactions generated by gauge invariant supercurrent multiplets which are bilinear in the superfield strength of the superspin $Y$ supermultiplet. We find two types of consistent supercurrents. The first one corresponds to conformal integer superspin $s$ supermultiplets, exist only for even values of $s, s=2\ell+2$, for arbitrary values of $Y$ and it is unique. The second one, corresponds to Poincar\'e integer superspin $s$ supermultiplets, exist for arbitrary values of $s$ and $Y$.