  Constructing a consistent four-dimensional Lagrangian for charged massive
higher-spin fields propagating in an electromagnetic background is an open
problem. In 1989, Argyres and Nappi used bosonic open string field theory to
construct a Lagrangian for charged massive spin-2 fields in a constant
electromagnetic background. In this paper, we use the four-dimensional hybrid
formalism for open superstring field theory to construct a supersymmetric
Lagrangian for charged massive spin-2 and spin-3/2 fields in a constant
electromagnetic background. The hybrid formalism has the advantage over the RNS
formalism of manifest $\mathcal{N}=1$ d=4 spacetime supersymmetry so that the
spin-2 and spin-3/2 fields are combined into a single superfield and there is
no need for picture-changing or spin fields.
