Topological Fields in $4d$ Higher Spin Theory

TL;DR

This paper investigates topological fields in 4d higher spin theory, demonstrating they have finite degrees of freedom and constructing a gauge-invariant cubic action for their interactions.

Contribution

It introduces a finite degrees of freedom framework for topological fields and develops a gauge-invariant cubic action for interacting higher spin fields.

Findings

Topological fields in 4d higher spin theory have finite degrees of freedom.

A gauge-invariant cubic action for interacting fields is constructed.

The work addresses the construction of gauge-invariant functionals.

Abstract

The equations for topological fields in the $4d$ higher spin theory are considered. It is shown that these fields contain a finite number of degrees of freedom that justifies their naming. The issue of construction of gauge invariant functionals is addressed, and a gauge-invariant cubic action is constructed for the interacting physical and topological higher spin fields.