General Cubic Interacting Vertex for Massless Integer Higher Spin Fields

TL;DR

This paper develops a comprehensive cubic interaction vertex for massless higher spin fields using the BRST approach, explicitly incorporating trace constraints to describe irreducible representations, and extends previous formulations with new derivative terms.

Contribution

It introduces a general off-shell cubic vertex for massless higher spin fields that includes trace constraints, expanding on prior models by adding derivative and non-derivative terms.

Findings

Constructed a complete cubic vertex including trace constraints.

Derived new terms with fewer derivatives and no derivatives.

Generalized previous cubic vertex formulations.

Abstract

We consider a massless higher spin field theory within the BRST approach and construct a general off-shell cubic vertex corresponding to irreducible higher spin fields of helicities $s_1, s_2, s_3$. Unlike the previous works on cubic vertices, which do not take into account of the trace constraints, we use the complete BRST operator, including the trace constraints that describe an irreducible representation with definite integer helicity. As a result, we generalize the cubic vertex found in [arXiv:1205.3131 [hep-th]] and calculate the new contributions to the vertex, which contain additional terms with a smaller number space-time derivatives of the fields as well as the terms without derivatives.