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

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arxiv 1701.08645 v3 pith:BG5PVU5M submitted 2017-01-30 hep-th

Thomas Basile , Roberto Bonezzi , Nicolas Boulanger This is my paper · ORCID
classification hep-th
keywords spin-stensorconnectioncompactconformalequationschoutenallows
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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.

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    A boundary-condition analysis of extended conformal gravity in 3D yields a new nonlinear W(2,2,2,2,1,1,1) asymptotic symmetry algebra whose central charges are fixed by the Virasoro central charge.

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