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

  • Thomas Basile
  • Roberto BonezziEmail author
  • Nicolas Boulanger
Open Access
Regular Article - Theoretical Physics


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 arXiv: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.


Conformal and W Symmetry Field Theories in Lower Dimensions Higher Spin Gravity Higher Spin Symmetry 


Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.


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Copyright information

© The Author(s) 2017

Authors and Affiliations

  • Thomas Basile
    • 1
    • 2
  • Roberto Bonezzi
    • 1
    Email author
  • Nicolas Boulanger
    • 1
  1. 1.Group of Mechanics and Gravitation, Physique théorique et mathématiqueUniversity of Mons - UMONSMonsBelgium
  2. 2.Laboratoire de Mathématiques et Physique Théorique, Unité Mixte de Recherche 7350 du CNRSFédération de Recherche 2964 Denis Poisson, Université François RabelaisToursFrance

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