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

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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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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Keywords

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