Homotopy Properties and Lower-Order Vertices in Higher-Spin Equations

TL;DR

This paper introduces a new homotopy method for analyzing nonlinear higher-spin equations, demonstrating its effectiveness in reproducing local interaction vertices and confirming their locality in four-dimensional theories without relying on background structures.

Contribution

A novel homotopy approach for higher-spin equations that directly reproduces local vertices and assesses their locality in a background-independent manner.

Findings

Successfully reproduces local vertices using the new approach

Confirms locality of cubic and quartic higher-spin vertices in 4D

Operates independently of background assumptions

Abstract

New homotopy approach to the analysis of nonlinear higher-spin equations is developed. It is shown to directly reproduce the previously obtained local vertices. Simplest cubic (quartic in Lagrangian nomenclature) higher-spin interaction vertices in four dimensional theory are examined from locality perspective by the new approach and shown to be local. The results are obtained in a background independent fashion.