Solving the Noether procedure for cubic interactions of higher spins in (A)dS

TL;DR

The paper develops a complete Noether-procedure framework for constructing cubic higher-spin interactions in (A)dS spaces using ambient-space formalism. It recasts the problem as solving polynomial PDEs for the TT part of the cubic vertices, organized by building blocks Y_i, Z_i and the AdS/CFT-relevant delta structure with the auxiliary parameter ûδ, and analyzes both massless and general massive (including partially-massless) cases. A key result is an explicit massless three-field AdS vertex given by an exponential operator acting on an arbitrary polynomial kernel, illustrating how curvature induces lower-derivative tails relative to flat space. The work connects bulk HS interactions to boundary CFT data via AdS/CFT intuition and provides a scalable method to classify all cubic HS couplings, with detailed solutions and a roadmap for handling more general mass configurations in (A)dS.

Abstract

The Noether procedure represents a perturbative scheme to construct all possible consistent interactions starting from a given free theory. In this note we describe how cubic interactions involving higher spins in any constant-curvature background can be systematically derived within this framework.