(A)dS exchanges and partially-massless higher spins

D. Francia; J. Mourad; A. Sagnotti

doi:10.1016/j.nuclphysb.2008.04.023

paper

(A)dS exchanges and partially-massless higher spins

arXiv:0803.3832 · doi:10.1016/j.nuclphysb.2008.04.023

Abstract

We determine the current exchange amplitudes for free totally symmetric tensor fields $\vf_{μ_1 ... μ_s}$ of mass $M$ in a $d$ -dimensional $d S$ 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 $d S$ 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 $d S$ radius. In general they are related to the hypergeometric functions $_{3} F_{2} (a, b, c; d, e; z)$ , 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 $A d S$ spaces can be obtained from these by a formal analytic continuation, while the massless limit is smooth, with no van Dam-Veltman-Zakharov discontinuity.

39 pages, LATEX. References added. Final version to appear in Nucl. Phys. B

(A)dS exchanges and partially-massless higher spins

Abstract

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