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

Thomas Basile (1) , Roberto Bonezzi , Nicolas Boulanger

1 LMPT - Laboratoire de Mathématiques et Physique Théorique

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.

Mots clés: Conformal and W Symmetry; Field Theories in Lower Dimensions; Higher Spin Gravity; Higher Spin Symmetry; gauge field theory: tensor; conformal; differential equations; cohomology; spin: high; dimension: 3; GL(5)

Domaines: Physique des Hautes Energies - Théorie [hep-th]

Thomas Basile, Roberto Bonezzi, Nicolas Boulanger. The Schouten tensor as a connection in the unfolding of 3D conformal higher-spin fields. Journal of High Energy Physics, 2017, 04, pp.054. ⟨10.1007/JHEP04(2017)054⟩. ⟨hal-01554762⟩