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arXiv · 1104.0722

On Dimensional Extension of Supersymmetry: From Worldlines to Worldsheets

S. J. Gates Jr.·T. Hubsch
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Abstract

There exist myriads of off-shell worldline supermultiplets for (N{\leq}32)-extended supersymmetry in which every supercharge maps a component field to precisely one other component field or its derivative. A subset of these extends to off-shell worldsheet (p,q)-supersymmetry and is characterized by the twin theorems 2.1 and 2.2 in this note. The evasion of the obstruction defined in these theorems is conjectured to be sufficient for a worldline supermultiplet to extend to worldsheet supersymmetry; it is also a necessary filter for dimensional extension to higher-dimensional spacetime. We show explicitly how to "re-engineer" an Adinkra---if permitted by the twin theorems 2.1 and 2.2---so as to depict an off-shell supermultiplet of worldsheet (p,q)-supersymmetry.

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S. J. Gates Jr., T. Hubsch. 2011-04-21. On Dimensional Extension of Supersymmetry: From Worldlines to Worldsheets. https://doi.org/10.4310/atmp.2012.v16.n6.a2

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