On $z$-dominance, shift symmetry and spin locality in higher-spin theory

TL;DR

This paper investigates the criteria for higher-spin locality, demonstrating that certain non-localities cancel out due to shift symmetry, supporting the conjecture of universal spin-locality in higher-spin theories.

Contribution

It proves the $z$-dominance conjecture by specifying conditions including shift symmetry, and defines admissible spin-local, shift-symmetric field redefinitions.

Findings

Validation of the $z$-dominance conjecture.

Identification of conditions ensuring spin-locality.

Definition of admissible field redefinitions respecting shift symmetry.

Abstract

The paper aims at the qualitative criterion of higher-spin locality. Perturbative analysis of the Vasiliev equations gives rise to the so-called $z$-dominated non-localities which nevertheless disappear from interaction vertices leaving the final result spin-local in all known cases. This has led one to the $z$ -- dominance conjecture that suggests universality of the observed cancellations. Here we specify conditions which include observation of the higher-spin shift symmetry and prove validity of this recently proposed conjecture. We also define a class of spin-local and shift-symmetric field redefinitions which is argued to be the admissible one with respect to spin-locality.