New 4D, N=1 superfield theory: model of free massive superspin-32 multiplet

We present a Lagrangian formulation for the free superspin-32 massive 4D, N=1 superfield. The model is described by a dynamical real vector superfield and an auxiliary real scalar superfield. The corresponding multiplet contains spin-1, spin-2 and two spin-32 propagating component fields on-shell. The auxiliary superfield is needed to ensure that the on-shell vector superfield carries only the irreducible representation of the Poincaré supergroup with a given mass and the fixed superspin of 32. The bosonic sector of the component level of the model is also presented.