Cubic interactions of Maxwell-like higher spins

TL;DR

This paper investigates cubic interaction vertices for Maxwell-like higher-spin fields in various backgrounds, revealing simplified, trace-free couplings that unify multiple spin interactions and extend to partially reducible systems.

Contribution

It introduces a systematic method for constructing cubic vertices for Maxwell-like higher spins, including extensions to partially reducible systems, using a novel Noether procedure approach.

Findings

Cubic vertices are trace-free and simpler than Fronsdal counterparts.

A unified description of interactions involving multiple spins.

Extension to partially reducible systems with trace constraints.

Abstract

We study the cubic vertices for Maxwell-like higher-spins in flat and (A)dS background spaces of any dimension. Reducibility of their free spectra implies that a single cubic vertex involving any three fields subsumes a number of couplings among different particles of various spins. The resulting vertices do not involve traces of the fields and in this sense are simpler than their Fronsdal counterparts. We propose an extension of both the free theory and of its cubic deformation to a more general class of partially reducible systems, that one can obtain from the original theory upon imposing trace constraints of various orders. The key to our results is a version of the Noether procedure allowing to systematically account for the deformations of the transversality conditions to be imposed on the gauge parameters at the free level.