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

Journal of High Energy Physics volume 2017, Article number: 54 (2017) Cite this article

A preprint version of the article is available at arXiv.

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 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.

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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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Authors and Affiliations

  1. Group of Mechanics and Gravitation, Physique théorique et mathématique, University of Mons - UMONS, 20 Place du Parc, 7000, Mons, Belgium

    Thomas Basile, Roberto Bonezzi & Nicolas Boulanger

  2. Laboratoire de Mathématiques et Physique Théorique, Unité Mixte de Recherche 7350 du CNRS, Fédération de Recherche 2964 Denis Poisson, Université François Rabelais, Parc de Grandmont, 37200, Tours, France

    Thomas Basile

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  1. Thomas Basile
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  2. Roberto Bonezzi
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Correspondence to Roberto Bonezzi.

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ArXiv ePrint: 1701.08645

Associate Researcher of the F.R.S.-FNRS (Belgium) (Nicolas Boulanger).

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Basile, T., Bonezzi, R. & Boulanger, N. The Schouten tensor as a connection in the unfolding of 3D conformal higher-spin fields. J. High Energ. Phys. 2017, 54 (2017). https://doi.org/10.1007/JHEP04(2017)054

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  • DOI: https://doi.org/10.1007/JHEP04(2017)054

Keywords

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