On the cubic interactions of massive and partially-massless higher spins in (A)dS

TL;DR

This work develops a covariant, ambient-space framework to classify all consistent cubic interactions of massive and partially-massless totally symmetric higher-spin fields in constant-curvature backgrounds. By focusing on traceless-transverse parts, the authors transform the Noether consistency conditions into PDEs that can be solved for fixed spin triplets, obtaining explicit $2$-$2$-$2$ and $3$-$3$-$2$ vertices and encoding general couplings via generating functions built from invariants like $Y_i$, $Z_i$, $G$ and their deformations. The Stückelberg formulation is integrated to study gauge invariance and massless limits, revealing how AdS and flat-space limits sculpt the leading interaction terms and how PM points constrain admissible couplings. The ambient-space method clarifies the structure of higher-spin interactions and connects with string-theoretic vertices and potential AdS/CFT realizations, while outlining directions to extend to fermions, mixed-symmetry fields, and higher-order consistency checks.

Abstract

Cubic interactions of massive and partially-massless totally-symmetric higher-spin fields in any constant-curvature background of dimension greater than three are investigated. Making use of the ambient-space formalism, the consistency condition for the traceless and transverse parts of the parity-invariant interactions is recast into a system of partial differential equations. The latter can be explicitly solved for given s_1-s_2-s_3 couplings and the 2-2-2 and 3-3-2 examples are provided in detail for general choices of the masses. On the other hand, the general solutions for the interactions involving massive and massless fields are expressed in a compact form as generating functions of all the consistent couplings. The Stückelberg formulation of the cubic interactions as well as their massless limits are also analyzed.