(A)dS exchanges and partially-massless higher spins

TL;DR

This work extends the framework of current exchanges to free massive totally symmetric higher-spin fields in de Sitter space by using an unconstrained, compensator-based formulation and a radial reduction from $(d+1)$-dimensional Minkowski space. It yields compact, rational expressions for exchange amplitudes in terms of $(ML)^2$ and generalized hypergeometric functions, with poles corresponding to partially massless states; in particular, the massless limit is smooth and the familiar vDVZ discontinuity disappears in the presence of a cosmological constant. A de Sitter dimensional reduction connects discrete spectrum states to gauge remnants, while the derived propagator forms offer multiple equivalent representations and facilitate unitarity considerations. Overall, the paper provides a comprehensive, technically explicit treatment of higher-spin current exchanges in $(A)dS$, laying groundwork for future investigations into interactions and unitarity in curved backgrounds.

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 $dS$ 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 $(ML)^2$, 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.