On hypersymmetry in three dimensions

Abstract

Abstract In this work we presented a number of explicit examples for the cubic vertices describing an interaction of massless spin-$$ \frac{5}{2} $$ 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 = $$ \frac{3}{3} $$ 3 3 , $$ \frac{1}{2} $$ 1 2 . Our general analysis predicted that the vertex must exist for any boson and fermion with the spin difference $$ \frac{3}{2} $$ 3 2 or $$ \frac{1}{2} $$ 1 2 . And indeed it appeared that the vertex exists for all six possible pairs (2, 1, 0) ⊗ ($$ \frac{3}{2} $$ 3 2 , $$ \frac{1}{2} $$ 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.