THE REAL ANATOMY OF COMPLEX LINEAR SUPERFIELDS

Abstract

Recent work on classification 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.