Spinor-helicity representations of (A)dS$_4$ particles of any mass

Abstract: The spinor-helicity representations of massive and (partially-)massless particles in four dimensional (Anti-) de Sitter spacetime are studied within the framework of the dual pair correspondence. We show that the dual groups (aka "little groups") of the AdS and dS groups are respectively $O(2N)$ and $O^*(2N)$. For $N=1$, the generator of the dual algebra $\mathfrak{so}(2)\cong \mathfrak{so}^*(2) \cong \mathfrak{u}(1)$ corresponds to the helicity operator, and the spinor-helicity representation describes massless particles in (A)dS$4$. For $N=2$, the dual algebra is composed of two ideals, $\mathfrak{s}$ and $\mathfrak{m}\Lambda$. The former ideal $\mathfrak{s}\cong \mathfrak{so}(3)$ fixes the spin of the particle, while the mass is determined by the latter ideal $\mathfrak{m}_\Lambda$, which is isomorphic to $\mathfrak{so}(2,1)$, $\mathfrak{iso}(2)$ or $\mathfrak{so}(3)$ depending on the cosmological constant being positive, zero or negative. In the case of a positive cosmological constant, namely dS$_4$, the spinor-helicity representation contains all massive particles corresponding to the principal series representations and the partially-massless particles corresponding to the discrete series representations leaving out only the light massive particles corresponding to the complementary series representations. The zero and negative cosmological constant cases, which had been addressed in earlier references, are also discussed briefly. Finally, we consider the multilinear form of helicity spinors invariant under (A)dS group, which can be served for the (A)dS counterpart of the scattering amplitude, and discuss technical differences and difficulties of the (A)dS cases compared to the flat spacetime case.