Hierarchy of Supersymmetric Higher Spin Connections

TL;DR

This paper develops a geometric hierarchy of superconnections for free higher spin supermultiplets in 4D N=1 superspace, introducing new formulations and constraints that unify and extend existing descriptions of higher spin supermultiplets.

Contribution

It introduces a hierarchy of superconnections with simple gauge transformations and explores new constrained and unconstrained formulations for higher spin supermultiplets in superspace.

Findings

Established a de Wit-Freedman like hierarchy of superconnections.

Discovered multiple constraints for decoupling superconnections.

Provided a new description of half-integer supermultiplets using compensators.

Abstract

We focus on the geometrical reformulation of free higher spin supermultiplets in $4\rm{D},~\mathcal{N}=1$ flat superspace. We find that there is a de Wit-Freedman like hierarchy of superconnections with simple gauge transformations. The requirement for sensible free equations of motion imposes constraints on the gauge parameter superfields. Unlike the nonsupersymmetric case, we find several different constraints that can decouple the higher superconnections. By lifting these constraints nongeometrically via compensators we recover all known descriptions of arbitrary integer and half-integer gauge supermultiplets. In the constrained formulation we find a new description of half-integer supermultiplets, generalizing the new-minimal and virial formulations of linearized supergravity to higher spins. However this description can be formulated using compensators. The various descriptions can be labeled as geometrical or nongeometrical if the equations of motion can be expressed purely in terms of superconnections or not.