All vertices for unconstrained symmetric gauge fields

TL;DR

This paper provides a comprehensive analysis of unconstrained symmetric higher-spin gauge field vertices, deriving their explicit form and dualities, and demonstrating their minimal locality and geometric integral structure across dimensions.

Contribution

It offers the first complete all-order formulation of unconstrained higher-spin vertices, including their dualities and geometric integral representation, for bosonic theories in any dimension.

Findings

Vertices are minimal, space-time local, and expressed as integrals over closed polygons.

Derived all-order manifest form of unconstrained vertices and their dualities.

Applied results to four-dimensional holomorphic higher-spin interactions, producing on-shell vertices.

Abstract

Recently, the generating system that describes interacting symmetric higher-spin gauge fields at the level of equations of motion was proposed. The interaction vertices it offers are 'off the mass shell' unless constrained by the prescribed factorization condition that properly removes traceful components. In this paper we detail the structure of the unconstrained, i.e., traceful vertices. We derive their manifest form to all orders along with a net of the associated dualities, thus providing the complete higher-spin vertex analysis at the unconstrained level for the bosonic theory in any dimension. These vertices are shown to be the minimal space-time local and have a form of the peculiar integrals over a space of closed polygons, which we scrutinize in the paper. The obtained results directly apply to the holomorphic sector of the four-dimensional theory, where the interaction is on shell, producing the all-order chiral higher-spin vertices.