On Nonlinear Higher Spin Curvature

TL;DR

This paper introduces the first nonlinear term of higher spin curvature, demonstrating its covariance under deformed gauge transformations, with detailed examples for spins 2 and 3, and generalization to arbitrary spin s.

Contribution

It provides the explicit form of the nonlinear higher spin curvature term, advancing the understanding of gauge invariance in higher spin theories.

Findings

First nonlinear higher spin curvature term derived

Covariance under deformed gauge transformations established

Explicit examples for spin 2 and 3, generalization to spin s

Abstract

We present the first nonlinear term of the higher spin curvature which is covariant with respect to deformed gauge transformations that are linear in the field. We consider in detail the case of spin 3 after presenting spin 2 as an example, and then construct the general spin s quadratic term of the deWit-Freedman curvature.