# The Schouten tensor as a connection in the unfolding of 3D conformal higher-spin fields

## TL;DR

This paper introduces a new first-order differential equation framework for 3D conformal higher-spin fields, connecting the Schouten tensor with a connection formalism to simplify the cohomological analysis.

## Contribution

It formulates a novel connection-based approach for conformal higher-spin fields in 3D, unifying the Schouten tensor and Cotton tensor within a compact differential equation framework.

## Key findings

- Reformulation of 3D conformal higher-spin equations as flatness conditions
- Explicit computational details for spin 3 and 4 cases
- General spin-s case presented in a compact form

## Abstract

A first-order differential equation is provided for a one-form, spin-s connection valued in the two-row, width-(s-1) Young tableau of GL(5). The connection is glued to a zero-form identified with the spin-s Cotton tensor. The usual zero-Cotton equation for a symmetric, conformal spin-s tensor gauge field in 3D is the flatness condition for the sum of the GL(5) spin-s and background connections. This presentation of the equations allows to reformulate in a compact way the cohomological problem studied in 1511.07389, featuring the spin-s Schouten tensor. We provide full computational details for spin 3 and 4 and present the general spin-s case in a compact way.