Off-shell construction of some trilinear higher spin gauge field interactions

TL;DR

This paper develops off-shell trilinear interactions for higher spin gauge fields, utilizing Noether's procedure, revealing connections to generalized Bell-Robinson tensors and extending previous work on higher even spins with conformal scalars.

Contribution

It introduces a systematic off-shell construction of trilinear higher spin interactions, including cases with derivative counts related to Bell-Robinson tensors and a tower of interactions with smaller spins.

Findings

Interactions involve currents from generalized Bell-Robinson tensors.

Finite tower of interactions with smaller even spins is established.

Results align with previous findings on higher even spins and conformal scalars.

Abstract

Several trilinear interactions of higher spin fields involving two equal ($s=s_{1}=s_{2}$) and one higher even ($s_{3}\geq 2s$) spin are presented. Interactions are constructed on the Lagrangian level using Noether's procedure together with the corresponding next to free level fields of the gauge transformations. In certain cases when the number of derivatives in the transformation is $2s-1$ the interactions lead to the currents constructed from the generalization of the gravitational Bell-Robinson tensors. In other cases when the number of derivatives in the transformation is more than $2s-1$ we obtain the finite tower of interactions with smaller even spins less than $s_{3}$ in full agreement with our previous results for the interaction of the higher even spins field with a conformal scalar [1,2].