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

TL;DR

This paper introduces a novel gauge theoretic approach to constructing twistors on 4D Riemannian manifolds using the conformal Cartan bundle and the dressing field method, offering a new perspective on conformally covariant structures.

Contribution

It presents a top-down gauge theoretic construction of twistors from the conformal Cartan bundle, utilizing the dressing field method to reveal their gauge fields and connections.

Findings

Constructed twistors as gauge fields via dressing method.

Provided BRST formulation for twistors.

Linked twistors to non-standard gauge objects.

Abstract

Tractors and Twistors bundles both 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 $\P$ and its vectorial $E$ and spinorial $\sE$ associated bundles. Our key ingredient is the dressing field method of gauge symmetry reduction, which allows to exhibit tractors and twistors and their associated connections as gauge fields of a non-standard kind as far as Weyl rescaling symmetry is concerned. By \emph{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.