On hypersymmetry in three dimensioons

TL;DR

This paper constructs explicit gauge-invariant cubic vertices describing interactions between massless spin-5/2 fields and various massive bosons and fermions in three dimensions, revealing the existence of such vertices for specific spin combinations.

Contribution

It provides explicit examples of gauge-invariant cubic vertices involving massless spin-5/2 fields and massive particles with spins 2, 1, 0, 3/2, and 1/2, expanding understanding of hypersymmetry interactions.

Findings

Vertices exist for all pairs with spin difference 3/2 or 1/2.

Vertices are invariant under gauge transformations of massive fields.

Explicit constructions confirm the predicted existence of these vertices.

Abstract

In this work we presented a number of explicit examples for the cubic vertices describing an interaction of massless spin-5/2 field with massive boson and fermion including all hypertransformations necessary for the vertices to be gauge invariant. Here we restrict ourselves with the massive bosons with spins s=2,1,0 and massive fermions with spins s=3/2,1/2. Our general analysis predicted that the vertex must exist for any boson and fermion with the spin difference 3/2 or 1/2. And indeed it appeared that the vertex exists for all six possible pairs (2,1,0) X (3/2,1/2). As in the case of massive supermultiplets, our construction is based on the gauge invariant description for the massive fields with spins s >= 1. Moreover, we have explicitly checked that all the vertices are invariant also under the gauge symmetries of these massive fields.