Homotopy Operators and Locality Theorems in Higher-Spin Equations

TL;DR

This paper introduces a new class of shifted homotopy operators in higher-spin gauge theory, formulates a locality condition, and proves a theorem identifying homotopies that reduce non-locality in perturbative expansions.

Contribution

It presents a novel class of homotopy operators and proves a theorem that helps control non-locality in higher-spin equations.

Findings

Introduction of shifted homotopy operators in higher-spin theory

Formulation of a locality condition for dynamical equations

Proof of Pfaffian Locality Theorem reducing non-locality

Abstract

A new class of shifted homotopy operators in higher-spin gauge theory is introduced. A sufficient condition for locality of dynamical equations is formulated and Pfaffian Locality Theorem identifying a subclass of shifted homotopies that decrease the degree of non-locality in higher orders of the perturbative expansion is proven.