A Superfield for Every Dash-Chromotopology

TL;DR

This paper proves that all adinkraic off-shell supermultiplets in N-extended worldline supersymmetry can be represented by superfields, linking a vast variety of supermultiplets to a smaller set of minimal ones.

Contribution

It completes the constructive proof that every supermultiplet in the classification scheme has a superfield representation, connecting complex supermultiplets to minimal foundational ones.

Findings

All supermultiplets have superfield representations.

Supermultiplets are related to a smaller set of minimal supermultiplets.

The classification scheme's supermultiplets are constructively linked to minimal supermultiplets.

Abstract

The recent classification scheme of so-called adinkraic off-shell supermultiplets of N-extended worldline supersymmetry without central charges finds a combinatorial explosion. Completing our earlier efforts, we now complete the constructive proof that all of these trillions or more of supermultiplets have a superfield representation. While different as superfields and supermultiplets, these are still super-differentially related to a much more modest number of minimal supermultiplets, which we construct herein.