Non-conformal higher spin supercurrents

Abstract

In four spacetime dimensions there exist two off-shell formulations for the massless multiplet of superspin $(s+\frac 12)$, where $s=2,3, \dots$. These supersymmetric higher spin gauge theories, known as longitudinal and transverse, are dual to each other and describe two massless fields of spin $(s+\frac 12)$ and $(s+1)$ upon elimination of the auxiliary fields. They respectively reduce, in the limiting case of $s=1$, to the linearised actions for the old minimal and the $n=-1$ non-minimal ${\cal N}=1$ supergravity theories. Associated with these gauge massless theories are non-conformal higher spin supercurrent multiplets which we describe. We demonstrate that the longitudinal higher spin supercurrents are realised in the model for a massive chiral scalar superfield only if $s$ is odd, $s=2n+1$, with $n= 1,2, \dots$.