English

Reduction Redux of Adinkras

High Energy Physics - Theory 2019-03-12 v2 Representation Theory

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, N\cal 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.

Keywords

Cite

@article{arxiv.1312.2000,
  title  = {Reduction Redux of Adinkras},
  author = {S. James Gates, and Stephen Randall and Kory Stiffler},
  journal= {arXiv preprint arXiv:1312.2000},
  year   = {2019}
}

Comments

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

R2 v1 2026-06-22T02:22:40.928Z