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

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.

24 pages, references added, paragraph added in proof

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• Conformal geometry and (super)conformal higher-spin gauge theories
• Topologically massive higher spin gauge theories
• Cubic interactions of arbitrary spin fields in 3d flat space
• Spin projection operators and higher-spin Cotton tensors in three dimensions
• One-loop effective actions and higher spins. II
• Conformal Higher-Spin Gravity: Linearized Spectrum = Symmetry Algebra
• Three-dimensional conformal geometry and prepotentials for four-dimensional fermionic higher-spin fields
• Higher-spin Cotton tensors and massive gauge-invariant actions in AdS${}_3$
• Superfield approach to interacting N=2 massive and massless supermultiplets in 3d flat space
• Enhanced Conformal $BM{S}_3$ Symmetries