Non-conformal higher spin supercurrents

TL;DR

This paper explores dual off-shell formulations of massless superspin multiplets in four dimensions, introduces associated non-conformal higher spin supercurrents, and reveals their realization conditions in massive chiral scalar superfield models.

Contribution

It provides a detailed description of dual formulations for superspin multiplets and characterizes the conditions for supercurrent realization in massive models.

Findings

Longitudinal supercurrents exist only for odd superspin values.

Dual formulations reduce to known supergravity theories for specific spins.

Supercurrents are linked to massive chiral scalar superfield models.

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 $n= 1,2, \dots$.