Lorentz covariance, higher-spin superspaces and self-duality

TL;DR

This paper develops Lorentz covariant extensions of supersymmetry, superspace, and self-duality, enabling the study of higher-spin fields and generalizing self-dual systems in a manifestly covariant framework.

Contribution

It introduces a novel Lorentz covariant framework for superspaces and self-duality, accommodating higher-spin fields and generalizing four-dimensional self-dual systems.

Findings

Framework allows for higher-spin superspaces with Lorentz covariance.

Constructs a hierarchy of solvable Lorentz covariant systems.

Provides a model for higher-dimensional, SO(3,1) covariant theories.

Abstract

Lorentz covariant generalisations of the notions of supersymmetry, superspace and self-duality are discussed. The essential idea is to extend standard constructions by allowing tangent vectors and coordinates which transform according to more general Lorentz representations than solely the spinorial and vectorial ones of standard lore. Such superspaces provide model configuration spaces for theories of arbitrary spin fields. Our framework is an elegant one for handling higher-dimensional theories in a manifestly SO(3,1) covariant fashion. A further application is the construction of a hierarchy of solvable Lorentz covariant systems generalising four-dimensional self-duality.