On interactions of massless integer high spin and scalar fields

TL;DR

This paper develops a new method to analyze interactions between massless integer higher spin fields and scalars, revealing that all local gauge-invariant vertices can be described using a specific symmetric tensor constructed from scalar fields.

Contribution

It introduces an unconstrained formulation and a novel deformation procedure to explicitly construct local interaction vertices involving higher spin and scalar fields.

Findings

Explicit construction of a symmetric tensor for cubic vertices.

Generalization to vertices of arbitrary order for spin 4.

Proof that all local gauge-invariant vertices involve this tensor.

Abstract

We apply an unconstrained formulation of bosonic higher spin fields to study interactions of these fields with a bosonic field using new method for the deformation procedure. It is proved that local vertices of any order containing one higher spin $s$ field and arbitrary number of scalar fields and being invariant under original gauge transformations are described with the help of one local totally symmetric $(s-2)$-rank tensor of scalar fields. This tensor is explicitly constructed for particular cases related to cubic vertices for spin $s$ and vertices of an arbitrary order for spin $s=4$.