Superconformal geometries and local twistors

TL;DR

This paper explores superconformal geometries across various spacetime dimensions using local supertwistor bundles, connecting them to standard superspace formalism and introducing local super Grassmannians as a new framework.

Contribution

It provides a unified description of superconformal geometries via supertwistor bundles, relates them to superspace formalism, and introduces local super Grassmannians as an alternative setting.

Findings

Superconformal geometries are described using local supertwistor bundles.

Gauge choices relate supertwistor formalism to standard superspace.

Introduction of local super Grassmannians offers a new perspective.

Abstract

Superconformal geometries in spacetime dimensions $D=3,4,{5}$ and $6$ are discussed in terms of local supertwistor bundles over standard superspace. These natually admit superconformal connections as matrix-valued one-forms. In order to make contact with the standard superspace formalism it is shown that one can always choose gauges in which the scale parts of the connection and curvature vanish, in which case the conformal and $S$-supersymmetry transformations become subsumed into super-Weyl transformations. The number of component fields can be reduced to those of the minimal off-shell conformal supergravity multiplets by imposing constraints which in most cases simply consists of taking the even covariant torsion two-form to vanish. This must be supplemented by further dimension-one constraints for the maximal cases in $D=3,4$. The subject is also discussed from a minimal point of view in which only the dimension-zero torsion is introduced. Finally, we introduce a new class of supermanifolds, local super Grassmannians, which provide an alternative setting for superconformal theories.