On holomorphic sector of higher-spin theory

TL;DR

This paper develops Vasiliev-like generating equations for holomorphic higher-spin interactions in four dimensions, ensuring space-time locality and revealing a shift symmetry, based on a contracted algebra approach.

Contribution

It introduces a new set of generating equations for holomorphic higher-spin interactions inspired by contracted algebra, enabling systematic extraction of all-order vertices.

Findings

Space-time locality of gauge fields is established.

Vertices exhibit a remarkable shift symmetry.

A systematic procedure for all-order holomorphic vertices is proposed.

Abstract

Recent investigation of locality problem for higher-spin fields led to a vertex reconstruction procedure that involved elements of contraction of the original Vasiliev interaction algebra. Inspired by these results we propose the Vasiliev-like generating equations for holomorphic higher-spin interactions in four dimensions based on the observed contracted algebra. We specify the functional class that admits evolution on the proposed equations and brings in a systematic procedure of extracting all-order holomorphic vertices. A simple consequence of the proposed equations is space-time locality of the gauge field sector. We also show that vertices come with a remarkable shift symmetry.