Supersymmetric Continuous Spin Gauge Theory

TL;DR

This paper develops a supersymmetric gauge theory for continuous spin particles, extending existing formulations and analyzing supersymmetry algebra closure and relations to higher spin theories.

Contribution

It provides the first supersymmetric extension of unconstrained and constrained continuous spin gauge field theories in four-dimensional flat space.

Findings

Supersymmetry transformations close on-shell.

Reproduction of higher spin gauge theory results in the helicity limit.

Relation between different supersymmetry formulations established.

Abstract

Taking into account the Schuster-Toro action and its fermionic analogue discovered by us, we supersymmetrize unconstrained formulation of the continuous spin gauge field theory. Afterwards, building on the Metsaev actions, we supersymmetrize constrained formulation of the theory. In each formulation, we provide supersymmetry transformations for the $\mathcal{N}=1$ supermultiplet in four-dimensional flat space-time, in which continuous spin particle (CSP) is considered to be a complex scalar continuous spin field, and its superpartner which can be called ``\,CSPino\,'' is considered to be a Dirac continuous spin field. It is shown that the algebra of these supersymmetry transformations are closed on-shell. Furthermore, we investigate whether obtained supersymmetry transformations reproduce the known result of the higher spin gauge field theory in the helicity limit. Finally, we illustrate how these two separate set of obtained transformations are related to each other.