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

TL;DR

This paper investigates cubic interactions among massive and partially-massless higher-spin fields in (A)dS spaces, providing explicit solutions and generating functions for consistent couplings, with analysis of St"uckelberg formulations and massless limits.

Contribution

It introduces a systematic method to solve for cubic interactions of higher-spin fields in (A)dS using ambient-space formalism, including explicit examples and generating functions.

Findings

Explicit solutions for 2-2-2 and 3-3-2 interactions.

Compact generating functions for all consistent couplings.

Analysis of St"uckelberg formulation and massless limits.

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 St\"uckelberg formulation of the cubic interactions as well as their massless limits are also analyzed.