# Tractors and twistors from conformal Cartan geometry: a gauge theoretic approach II. Twistors

2 CPT - E2 Géométrie, Physique et Symétries
CPT - Centre de Physique Théorique - UMR 7332
Abstract : Tractor and Twistor bundles provide natural conformally covariant calculi on 4D-Riemannian manifolds. They have different origins but are closely related, and usually constructed bottom–up through prolongation of defining differential equations. We propose alternative top–down gauge theoretic constructions, starting from the conformal Cartan bundle $\mathcal{P}$ and its vectorial E and spinorial ${\mathsf {E}}$ associated bundles. Our key ingredient is the dressing field method of gauge symmetry reduction, which allows tractors and twistors and their associated connections to exhibit as gauge fields of a non-standard kind as far as Weyl rescaling transformation is concerned. By non-standard we mean that they implement the gauge principle of physics, but are of a different geometric nature than the well-known differential geometric objects usually underlying gauge theories. We provide the corresponding BRST treatment. In a companion paper we dealt with tractors, in the present one we address the case of twistors.
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Article dans une revue
Classical and Quantum Gravity, IOP Publishing, 2017, 34 (8), pp.085004. 〈10.1088/1361-6382/aa627d〉

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https://hal.archives-ouvertes.fr/hal-01494144
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Dernière modification le : vendredi 20 juillet 2018 - 13:44:06
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François Jordan, Jérémy Attard, J. François. Tractors and twistors from conformal Cartan geometry: a gauge theoretic approach II. Twistors. Classical and Quantum Gravity, IOP Publishing, 2017, 34 (8), pp.085004. 〈10.1088/1361-6382/aa627d〉. 〈hal-01494144〉

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