image exchanges and partially-massless higher spins Original Research Article

We determine the current exchange amplitudes for free totally symmetric tensor fields image of mass M in a d-dimensional dS space, extending the results previously obtained for image by other authors. Our construction is based on an unconstrained formulation where both the higher-spin gauge fields and the corresponding gauge parameters image are not subject to Fronsdalʹs trace constraints, but compensator fields image are introduced for image. The free massive dS equations can be fully determined by a radial dimensional reduction from a image-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 image dimensions, but are otherwise arbitrary. As for image, these amplitudes are rational functions of image, where L is the dS radius. In general they are related to the hypergeometric functions image, 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.