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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 $frac{8}{3}(s+1)(4s^2+11s+3)$.
In recent papers we demonstrated that consistent and non-trivial emph{linear} transformations of matter supermultiplets generate half-integer superspin supercurrents and the cubic interactions between matter and half-integer superspin supermultiplets
Free massless higher-superspin superfields on the N=1, D=4 anti-de Sitter superspace are introduced. The linearized gauge transformations are postulated. Two families of dually equivalent gauge-invariant action functionals are constructed for massles
Observables of topological Yang-Mills theory were defined by Witten as the classes of an equivariant cohomology. We propose to define them alternatively as the BRST cohomology classes of a superspace version of the theory, where BRST invariance is as
Action of 4 dimensional N=4 supersymmetric Yang-Mills theory is written by employing the superfields in N=4 superspace which were used to prove the equivalence of its constraint equations and equations of motion. Integral forms of the extended supers
Lagrangians for several new off-shell 4D, N = 1 supersymmetric descriptions of massive superspin-1 and superspin-3/2 multiplets are described. Taken together with the models previously constructed, there are now four off-shell formulations for the ma