Analysis of Higher Spin Field Equations in Four Dimensions

TL;DR

This work analyzes a four-dimensional minimal bosonic HS gauge theory built on an infinite extension of $AdS_4$ (Vasiliev-like). It develops a curvature-expansion method that treats gravity exactly and HS fields perturbatively, and provides an explicit iterative procedure to derive the full set of master-field equations to arbitrary curvature order, including detailed quadratic terms. It also clarifies the relationship to Vasiliev's ${\cal N}=2$ model via consistent truncation to the $hs(4)$ spectrum, and establishes a Lorentz-covariant framework with a physical gauge and a decomposition of the master field into gravitational and HS sectors. The results lay groundwork for HS holography with the boundary scalar singleton and for potential actions and boundary correlator computations.

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.