9464 1810.04457 10.1007/JHEP11(2018)156 156 156 Three-dimensional conformal geometry and prepotentials for four-dimensional fermionic higher-spin fields Regular Article - Theoretical Physics 1 28 2018 11 23 2018 10 14 2018 11 13 2018 11 23 The Author(s) 2018 13130 2018 2018 11 11 Marc Henneaux henneaux@ulb.ac.be Victor Lekeu vlekeu@ulb.ac.be Amaury Leonard amaury.leonard@ulb.ac.be Javier Matulich jmatulic@ulb.ac.be Stefan Prohazka stefan.prohazka@ulb.ac.be 0000 0001 2348 0746 grid.4989.c Université Libre de Bruxelles and International Solvay Institutes Campus Plaine — CP 231 B-1050 Bruxelles Belgium 0000 0001 2113 8111 grid.7445.2 The Blackett Laboratory Imperial College London Prince Consort Road London SW7 2AZ U.K. 0000 0001 0790 4262 grid.450243.4 Max-Planck-Institut für Gravitationsphysik (Albert-Einstein-Institut) Am Mühlenberg 1 DE-14476 Potsdam Germany Abstract We introduce prepotentials for fermionic higher-spin gauge fields in four space-time 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. Keywords Higher Spin Symmetry Gauge Symmetry Supersymmetry and Duality ArXiv ePrint: 1810.04457 On leave of absence from Collège de France, Paris. (Marc Henneaux)