4D, N = 1 Supersymmetry Genomics (I)

A Unified Enumeration of 1-dimension Garden Algebras and Valise Adinkras

In the study of supersymmetry in one dimension, various works enumerate sets of generators of garden algebras $GR(d,N)$ (and equivalently, valise Adinkras) for special cases $N = d = 4$ and $N = d = 8$, using group-theoretic methods and computer computation. We complement this work by enumerating the objects for arbitrary $N$ and $d$ via a formula in a streamlined manner.

Think Different: Applying the Old Macintosh Mantra to the Computability of the SUSY Auxiliary Field Problem

Starting with valise supermultiplets obtained from 0-branes plus field redefinitions, valise adinkra networks, and the "Garden Algebra," we discuss an architecture for algorithms that (starting from on-shell theories and, through a well-defined computation procedure), search for off-shell completions. We show in one dimension how to directly attack the notorious "off-shell auxiliary field" problem of supersymmetry with algorithms in the adinkra network-world formulation.

A Note On Exemplary Off-Shell Constructions Of 4D, ${\mathbf {\cal N}}$ = 2 Supersymmetry Representations

We continue the search for rules that govern when off-shell 4D, $\cal N$ = 1 supermultiplets can be combined to form off-shell 4D, $\cal N$ = 2 supermultiplets. We study the ${\mathbb S}_8$ permutations and Height Yielding Matrix Numbers (HYMN) embedded within the adinkras that correspond to these putative 4D, $\cal N$ = 2 supermultiplets off-shell supermultiplets. Even though the HYMN definition was designed to distinguish between the raising and lowering of nodes in one dimensional valises supermultiplets, they are shown to accurately select out which combinations of off-shell 4D, $\cal N$ =…

扩展/高维SUSY Holoraumy中Valise与在壳超多重态表示的无限维代数$\mathfrak{Spin}$($N$)结构

Infinite-Dimensional Algebraic $\mathfrak{Spin}$($N$) Structure in Extended/Higher Dimensional SUSY Holoraumy for Valise and On-Shell Supermultiplet Representations

本文研究高维超对称中holoraumy与Hodge对偶的关系，发现六维以上该关系非必需，但四维矢量-张量多重态中存在，且约化到一维揭示与扩展$\mathfrak{Spin}(N)$的无限维代数相关。

Adinkra 高度生成矩阵数：最小四色 Adinkra 的特征值等价类

Adinkra Height Yielding Matrix Numbers: Eigenvalue Equivalence Classes for Minimal Four-Color Adinkras

本文通过 Python 代码将特征值等价类从 valise Adinkra 扩展到非 valise Adinkra，为 36,864 个与 Coxeter 群 BC4 相关的 Adinkra 提供完整分类，引入 HYMN 等价类，并发布在 HEPTHools 数据仓库。

4D, N = 1 Supersymmetry Genomics (II)

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.