The Real Anatomy of Complex Linear Superfields

TL;DR

This paper analyzes the complex linear supermultiplet in off-shell supersymmetry, revealing it is not adinkraic and cannot be decomposed locally, thus suggesting a much larger diversity of supersymmetry representations than previously thought.

Contribution

It provides an explicit analysis showing that the complex linear supermultiplet is not adinkraic and cannot be decomposed locally, expanding understanding of supersymmetry representation diversity.

Findings

Complex linear supermultiplet is not adinkraic.

Cannot decompose the supermultiplet locally.

Can be reduced via a Wess-Zumino gauge.

Abstract

Recent work on classicication of off-shell representations of N-extended worldline supersymmetry without central charges has uncovered an unexpectedly vast number--trillions of even just (chromo)topology types--of so called adinkraic supermultiplets. Herein, we show by explicit analysis that a long-known but rarely used representation, the complex linear supermultiplet, is not adinkraic, cannot be decomposed locally, but may be reduced by means of a Wess-Zumino type gauge. This then indicates that the already unexpectedly vast number of adinkraic off-shell supersymmetry representations is but the proverbial tip of the iceberg.