Analysis of Higher Spin Field Equations in Four Dimensions

TL;DR

This paper develops an expansion scheme for analyzing higher spin gauge theories in four dimensions, treating gravitational fields exactly and perturbing higher spin fields, with detailed iterative procedures for deriving field equations.

Contribution

It introduces a novel expansion method that treats gravitational gauge fields exactly while handling higher spin fields as perturbations, providing a systematic way to derive higher order field equations.

Findings

Explicit iteration procedure for field equations to arbitrary order.

Detailed structure of quadratic terms in the higher spin field equations.

A new expansion scheme for higher spin gauge theories in four dimensions.

Abstract

The minimal bosonic higher spin gauge theory in four dimensions contains massless particles of spin s=0,2,4,.. that arise in the symmetric product of two spin 0 singletons. It is based on an infinite dimensional extension of the AdS_4 algebra a la Vasiliev. We derive an expansion scheme in which the gravitational gauge fields are treated exactly and the gravitational curvatures and the higher spin gauge fields as weak perturbations. We also give the details of an explicit iteration procedure for obtaining the field equations to arbitrary order in curvatures. In particular, we highlight the structure of all the quadratic terms in the field equations.