4D, N = 1 Supersymmetry Genomics (II)

TL;DR

This paper advances the understanding of off-shell 4D, N=1 supersymmetric representations by identifying fundamental building blocks called cis- and trans-Adinkras, and analyzing specific superfield multiplets to determine their composition.

Contribution

It introduces a framework for decomposing supersymmetric representations into cis- and trans- components and applies it to specific superfield multiplets, revealing their structural composition.

Findings

Real scalar superfield has n_c = n_t = 1.

Complex linear superfield has n_c = 1, n_t = 2.

Supersymmetric representations can be viewed as composites of cis- and trans-Adinkras.

Abstract

We continue the development of a theory of off-shell supersymmetric representations analogous to that of compact Lie algebras such as SU(3). For off-shell 4D, N = 1 systems, quark-like representations have been identified [1] in terms of cis-Adinkras and trans-Adinkras and it has been conjectured that arbitrary representations are composites of $n_c$-cis and $n_t$-trans representations. Analyzing the real scalar and complex linear superfield multiplets, these "chemical enantiomer" numbers are found to be $n_c$ = $n_t$ = 1 and $n_c$ = 1, $n_t$ = 2, respectively.