Unfolded Adinkra Properties of Supermultiplets (I)

Abstract

Adinkra networks arise in the Carroll limit of supersymmetric QFT. Extensions of adinkras that are infinite dimensional graphs have never previously been discussed in the literature. We call these "infinite unfolded'' adinkras and study the properties of their realization on familiar 4D, $\cal N$ = 1 supermultiplets. A new feature in "unfolded'' adinkras is the appearance of quantities whose actions resemble BRST operators within Verma-like modules. New "net-centric" quantities ${\widetilde \chi}_{(1)}$ and ${\widetilde \chi}_{(2)}$ are introduced, which along with quantity $\chi_{\rm o}$, describe distinctions between familiar supermultiplets in 4D, $\cal N $ = 1 theories. A previously unobserved property in all adinkras that we call "adinkra vorticity" is noted.