Three-dimensional conformal geometry and prepotentials for four-dimensional 
fermionic higher-spin fields

Henneaux, Marc; Lekeu, Victor; Leonard , Amaury; Matulich, Javier; Prohazka, Stefan

doi:10.1007/JHEP11(2018)156

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Three-dimensional conformal geometry and prepotentials for four-dimensional fermionic higher-spin fields

MPS-Authors

Leonard , Amaury
AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Citation

Henneaux, M., Lekeu, V., Leonard, A., Matulich, J., & Prohazka, S. (2018). Three-dimensional conformal geometry and prepotentials for four-dimensional fermionic higher-spin fields. Journal of High Energy Physics, 2018(11): 156. doi:10.1007/JHEP11(2018)156.

Cite as: https://hdl.handle.net/21.11116/0000-0002-6924-0

Abstract

We introduce prepotentials for fermionic higher-spin gauge fields in four
spacetime dimensions, generalizing earlier work on bosonic fields. To that end,
we first develop tools for handling conformal fermionic higher-spin gauge
fields in three dimensions. This is necessary because the prepotentials turn
out to be three-dimensional fields that enjoy both "higher-spin diffeomorphism"
and "higher-spin Weyl" gauge symmetries. We discuss a number of the key
properties of the relevant Cotton tensors. The reformulation of the equations
of motion as "twisted self-duality conditions" is then exhibited. We show next
how the Hamiltonian constraints can be explicitly solved in terms of
appropriate prepotentials and show that the action takes then the same
remarkable form for all spins.