Abstract
We determine the current exchange amplitudes for free totally symmetric tensor fields φ μ 1 … μ s of mass M in a d-dimensional dS space, extending the results previously obtained for s = 2 by other authors. Our construction is based on an unconstrained formulation where both the higher-spin gauge fields and the corresponding gauge parameters Λ μ 1 … μ s − 1 are not subject to Fronsdal's trace constraints, but compensator fields α μ 1 … μ s − 3 are introduced for s > 2 . The free massive dS equations can be fully determined by a radial dimensional reduction from a ( 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 ) dimensions, but are otherwise arbitrary. As for s = 2 , these amplitudes are rational functions of ( M L ) 2 , where L is the dS radius. In general they are related to the hypergeometric functions F 2 3 ( 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.
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