Perturbative analysis in higher-spin theories

TL;DR

This paper introduces a simplified perturbative scheme for higher-spin theories that streamlines calculations by reducing complex integrals, enabling direct derivation of key theorems from nonlinear equations.

Contribution

A novel perturbative analysis method for higher-spin equations that simplifies computations using spectral sequences and reduces multiple integrals to a single integral.

Findings

Method simplifies higher-spin perturbation calculations.

Enables direct derivation of the Central on-shell theorem.

Illustrated with various examples demonstrating efficiency.

Abstract

A new scheme of the perturbative analysis of the nonlinear HS equations is developed giving directly the final result for the successive application of the homotopy integrations which appear in the standard approach. It drastically simplifies the analysis and results from the application of the standard spectral sequence approach to the higher-spin covariant derivatives, allowing us in particular to reduce multiple homotopy integrals resulting from the successive application of the homotopy trick to a single integral. Efficiency of the proposed method is illustrated by various examples. In particular, it is shown how the Central on-shell theorem of the free theory immediately results from the nonlinear HS field equations with no intermediate computations.