Copyright © 2011 M. G. Faux et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We explain how the representation theory associated with supersymmetry in diverse dimensions is encoded within the representation theory of supersymmetry in one time-like dimension. This is enabled by algebraic criteria, derived, exhibited, and utilized in this paper, which indicate which subset of one-dimensional supersymmetric models describes “shadows” of higher-dimensional models. This formalism delineates that minority of one-dimensional supersymmetric models which can “enhance” to accommodate extra dimensions. As a consistency test, we use our formalism to reproduce well-known conclusions about supersymmetric field theories using one-dimensional reasoning exclusively. And we introduce the notion of “phantoms” which usefully accommodate higher-dimensional gauge invariance in the context of shadow multiplets in supersymmetric quantum mechanics.