Superspace formulation of massive half-integer superspin

TL;DR

This paper derives an explicit superspace Lagrangian for massive half-integer superspin supermultiplets in 4D, introducing auxiliary superfields and analyzing their decoupling in the massless limit.

Contribution

It provides a new superspace formulation for massive half-integer superspin supermultiplets with a systematic auxiliary superfield tower.

Findings

Explicit Lagrangian formulation in superspace

Auxiliary superfields decouple in the massless limit

Off-shell degrees of freedom quantified

Abstract

An explicit form for the lagrangian of an arbitrary half-integer superspin ${\textsf{Y}}=s+1/2$ supermultiplet is obtained in $4{\rm D},~\mathcal{N}=1$ superspace. This is accomplished by the introduction of a tower of pairs of auxiliary superfields of increasing rank which are required to vanish on-shell for free theories. In the massless limit almost all auxiliary superfields decouple except one, which plays the role of compensator as required by the emergent gauge redundancy of the Lagrangian description of the massless theory. The number of off-shell degrees of freedom carried by the theory is $\frac{8}{3}(s+1)(4s^2+11s+3)$.