Supersymmetric Lorentz-Covariant Hyperspaces and self-duality equations in dimensions greater than (4|4)

TL;DR

This paper introduces generalized superspaces called hyperspaces with higher dimensions and Lorentz covariance, and derives new self-duality equations that are solvable, extending traditional supersymmetry concepts.

Contribution

It develops a framework for superspaces with broader Lorentz representations and constructs new self-duality equations in these higher-dimensional hyperspaces.

Findings

Defined novel SO(3,1)-covariant hyperspaces with higher dimensions.

Derived classes of solvable self-duality equations in complexified hyperspaces.

Extended supersymmetry notions beyond standard super-Minkowski space.

Abstract

We generalise the notions of supersymmetry and superspace by allowing generators and coordinates transforming according to more general Lorentz representations than the spinorial and vectorial ones of standard lore. This yields novel SO(3,1)-covariant superspaces, which we call hyperspaces, having dimensionality greater than (4|4) of traditional super-Minkowski space. As an application, we consider gauge fields on complexifications of these superspaces; and extending the concept of self-duality, we obtain classes of completely solvable equations analogous to the four-dimensional self-duality equations.