Reduction Redux of Adinkras

Abstract

We show performing general "0-brane reduction" along an arbitrary fixed direction in spacetime and applied to the starting point of minimal, off-shell 4D, $\mathcal{N}$ $=$ 1 irreducible supermultiplets, yields adinkras whose adjacency matrices are among some of the special cases proposed by Kuznetsova, Rojas, and Toppan. However, these more general reductions also can lead to `Garden Algebra' structures beyond those described in their work. It is also shown that for light-like directions, reduction to the 0-brane breaks the equality in the number of fermions and bosons for dynamical theories. This implies that light-like reductions should be done instead to the space of 1-branes or equivalently to the worldsheet.

17 pages, corrected reference, added note at the end, various typo corrections

Cited by in corpus (4)

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• Adinkra `Color' Confinement In Exemplary Off-Shell Constructions Of 4D, $\mathcal{N}$ = 2 Supersymmetry Representations
• Think Different: Applying the Old Macintosh Mantra to the Computability of the SUSY Auxiliary Field Problem