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It is known that the spin-3/2 field in N-dimensional de Sitter space (dS_N) becomes gauge invariant (i.e. massless) for a specific mass-cosmological constant tuning, for which the mass parameter is purely imaginary. In this talk, I will present some previously unknown group-theoretic features of the massless spin-3/2 field (i.e. gravitino field) theory in dS_N. In particular, by studying the way in which the gravitino eigenmodes form representations of the de Sitter algebra spin(N,1) (with N>2), I show that: i) For even N>4: both positive- and negative-norm eigenmodes exist and they inevitably transform into each other under spin(N,1). ii) For N=4: the eigenmodes are separated into two spin(4,1)-invariant subspaces, for both of which the norm can be chosen to be positive. One subspace contains positive-helicity states and the other negative-helicity states. iii) For odd N: there does not exist any de Sitter invariant scalar product for the eigenmodes that is not identically zero and, thus, the spin(N,1) representation is, by definition, non-unitary. The analysis presented in this talk shows that the gravitino field theory is unitary only in 4-dimensional de Sitter space.

Zoomformation: https://ucdavis.zoom.us/j/98158437429