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(A)dS exchanges and partially-massless higher spins

D. Francia J. Mourad 1 A. Sagnotti
APC (UMR_7164) - AstroParticule et Cosmologie, Institut für theoretische Physik
Abstract : We determine the current exchange amplitudes for free totally symmetric tensor fields $\vf_{\mu_1 ... \mu_s}$ 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 $\Lambda_{\mu_1 >... \mu_{s-1}}$ are not subject to Fronsdal's trace constraints, but compensator fields $\alpha_{\mu_1 ... \mu_{s-3}}$ 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 $(ML)^2$, where $L$ is the $dS$ radius. In general they are related to the hypergeometric functions $_3F_2(a,b,c;d,e;z)$, 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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Submitted on : Thursday, April 17, 2008 - 3:06:36 PM
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D. Francia, J. Mourad, A. Sagnotti. (A)dS exchanges and partially-massless higher spins. Nuclear Physics B, Elsevier, 2008, ⟨10.1016/j.nuclphysb.2008.04.023⟩. ⟨in2p3-00274203⟩



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