Constructing the Cubic Interaction Vertex of Higher Spin Gauge Fields

TL;DR

This paper introduces a systematic method using oscillator formalism and BRST techniques to construct cubic interaction vertices for massless Higher Spin gauge fields in flat and AdS spaces, advancing towards a full interacting theory.

Contribution

It generalizes the Higher Spin symmetry algebra to include cubic interactions and provides a framework applicable to arbitrary dimensions and orders.

Findings

Derived general conditions for cubic interaction vertices.

Discussed ambiguities due to field redefinitions.

Established a foundation for constructing interacting Higher Spin theories.

Abstract

We propose a method of construction of a cubic interaction in massless Higher Spin gauge theory both in flat and in AdS space-times of arbitrary dimensions. We consider a triplet formulation of the Higher Spin gauge theory and generalize the Higher Spin symmetry algebra of the free model to the corresponding algebra for the case of cubic interaction. The generators of this new algebra carry indexes which label the three Higher Spin fields involved into the cubic interaction. The method is based on the use of oscillator formalism and on the Becchi-Rouet-Stora-Tyutin (BRST) technique. We derive general conditions on the form of cubic interaction vertex and discuss the ambiguities of the vertex which result from field redefinitions. This method can in principle be applied for constructing the Higher Spin interaction vertex at any order. Our results are a first step towards the construction of a Lagrangian for interacting Higher Spin gauge fields that can be holographically studied.