  The interactions that can be introduced between a massless Rarita-Schwinger
field and an Abelian three-form gauge field in eleven spacetime dimensions are
analyzed in the context of the deformation of the free solution of the master
equation combined with local BRST cohomology. Under the hypotheses of
smoothness of the interactions in the coupling constant, locality, Poincare
invariance, Lorentz covariance, and the presence of at most two derivatives in
the Lagrangian of the interacting theory (the same number of derivatives like
in the free Lagrangian), we prove that there are neither cross-couplings nor
self-interactions for the gravitino in D=11.The only possible term that can be
added to the deformed solution to the master equation is nothing but a
generalized Chern-Simons term for the three-form gauge field, which brings
contributions to the deformed Lagrangian, but does not modify the original,
Abelian gauge transformations.
