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The cross-couplings among several massless spin-two fields (described in thefree limit by a sum of Pauli-Fierz actions) in the presence of a massiveRarita-Schwinger field are investigated in the framework of the deformationtheory 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 eachfield, we prove that there are no consistent cross-interactions among differentgravitons with a positively defined metric in internal space in the presence ofa massive Rarita-Schwinger field. The basic features of the couplings between asingle Pauli-Fierz field and a massive Rarita-Schwinger field are alsoemphasized.

No interactions for a collection of spin-two fields intermediated by a massive Rarita-Schwinger field