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Dimensional Enhancement via Supersymmetry

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  • M. G. Faux
  • K. M. Iga
  • G. D. Landweber

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.

Suggested Citation

  • M. G. Faux & K. M. Iga & G. D. Landweber, 2011. "Dimensional Enhancement via Supersymmetry," Advances in Mathematical Physics, Hindawi, vol. 2011, pages 1-45, October.
    • Handle: RePEc:hin:jnlamp:259089
    DOI: 10.1155/2011/259089
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