Superspace: a Comfortably Vast Algebraic Variety

TL;DR

This paper establishes the fundamental existence of superspace, clarifies its algebraic structure, and highlights its significance in supersymmetry, providing a comprehensive mathematical foundation for its applications.

Contribution

The paper proves the existence of superspace and explores its algebraic and geometric properties, resolving longstanding doubts and advancing the mathematical understanding of supersymmetry.

Findings

Superspace must exist, resolving previous doubts.

Superspace has a large, rich algebraic and geometric structure.

The study clarifies the role of superspace in supersymmetry applications.

Abstract

Supersymmetry has been studied for over three decades by physicists, its superset even longer by mathematicians, and superspace has proven to be very useful both conceptually and in facilitating computations. However, the (1) necessary existence of superspace has been doubted, and its (2) properties and (3) applications have not been understood in general. Herein, all doubt is removed from the first of these: superspace must exist. Further study then reveals a perhaps surprising size and algebro-geometric structure of this extension of spacetime.