On Massive High Spin Particles in (A)dS

TL;DR

This work develops a gauge-invariant description of massive higher-spin fields in $(A)dS$ by coupling a tower of Stueckelberg-like fields and enforcing invariance to derive unitarity and partial masslessness properties. It derives explicit parameter relations and the cosmological-constant dependent critical masses for spins 2 and 3, and generalizes to arbitrary spin $s$ in dimension $d$, culminating in a main result for $\alpha_k^2 = \frac{(s-k)(s+k+d-3)}{(k+1)(2k+d-2)}\big[m^2 - \Omega (s-k-1)(s+k+d-4)\big]$ with $\Omega=\frac{2\Lambda}{(d-1)(d-2)}$, which encodes all partially massless points. The findings reproduce the Deser–Waldron conjecture in $d=4$ and clarify how partial masslessness emerges via decoupling of sectors at critical $\Lambda$ values, shedding light on unitarity, gauge invariance, and the structure of higher-spin theories in curved backgrounds.

Abstract

In this Letter we consider the problem of partial masslessness and unitarity in (A)dS using gauge invariant description of massive high spin particles. We show that for S = 2 and S = 3 cases such formalism allows one correctly reproduce all known results. Then we construct a gauge invariant formulation for massive particles of arbitrary integer spin s in arbitrary space-time dimension d. For d = 4 our results confirm the conjecture made recently by Deser and Waldron.