Self-duality in Generalized Lorentz Superspaces

TL;DR

This paper generalizes the concept of self-duality to Lorentz superspaces constructed from various representations, extending beyond traditional super Minkowski space, and defines a new form of gauge curvature conditions.

Contribution

It introduces a novel framework for self-duality in generalized Lorentz superspaces with superalgebra structures, broadening the scope of gauge theories in supersymmetric contexts.

Findings

Defines generalized self-duality conditions in Lorentz superspaces.

Extends the notion of gauge curvature to superspaces with diverse representations.

Provides a foundation for future studies of gauge theories in extended supersymmetric geometries.

Abstract

We extend the notion of self-duality to spaces built from a set of representations of the Lorentz group with bosonic or fermionic behaviour, not having the traditional spin-one upper-bound of super Minkowski space. The generalized derivative vector fields on such superspaces are assumed to form a superalgebra. Introducing corresponding gauge potentials and hence covariant derivatives and curvatures, we define generalized self-duality as the Lorentz covariant vanishing of certain irreducible parts of the curvatures.