(A)dS(A)dS exchanges and partially-massless higher spins

We determine the current exchange amplitudes for free totally symmetric tensor fields φμ1…μsφμ1…μs of mass M in a d-dimensional dS   space, extending the results previously obtained for s=2s=2 by other authors. Our construction is based on an unconstrained formulation where both the higher-spin gauge fields and the corresponding gauge parameters Λμ1…μs−1Λμ1…μs−1 are not subject to Fronsdal's trace constraints, but compensator fields αμ1…μs−3αμ1…μs−3 are introduced for s>2s>2. The free massive dS   equations can be fully determined by a radial dimensional reduction from a (d+1)(d+1)-dimensional Minkowski space time, and lead for all spins to relatively handy closed-form expressions for the exchange amplitudes, where the external currents are conserved, both in d   and in (d+1)(d+1) dimensions, but are otherwise arbitrary. As for s=2s=2, these amplitudes are rational functions of (ML)2(ML)2, where L is the dS   radius. In general they are related to the hypergeometric functions F23(a,b,c;d,e;z), and their poles identify a subset of the “partially-massless” discrete states, selected by the condition that the gauge transformations of the corresponding fields contain some non-derivative terms. Corresponding results for AdS spaces can be obtained from these by a formal analytic continuation, while the massless limit is smooth, with no van Dam–Veltman–Zakharov discontinuity.