  The cross-couplings among several massless spin-two fields (described in the
free limit by a sum of Pauli-Fierz actions) in the presence of a massive
Rarita-Schwinger field are investigated in the framework of the deformation
theory based on local BRST cohomology. Under the hypotheses of locality,
smoothness of the interactions in the coupling constant, Poincare invariance,
Lorentz covariance, and the preservation of the number of derivatives on each
field, we prove that there are no consistent cross-interactions among different
gravitons with a positively defined metric in internal space in the presence of
a massive Rarita-Schwinger field. The basic features of the couplings between a
single Pauli-Fierz field and a massive Rarita-Schwinger field are also
emphasized.
