4D, N = 1 Supersymmetry Genomics (I)

TL;DR

This paper explores the representation theory of 4D, N=1 supersymmetry using Adinkras and Garden Algebras, revealing fundamental structures and proposing a classification conjecture based on valise Adinkras.

Contribution

It introduces a novel graphical approach to supersymmetry representations and proposes a conjecture linking supermultiplet descriptions to pairs of fundamental Adinkras.

Findings

Identification of two fundamental valise Adinkras: cis-Valise and trans-Valise.

Survey of matter multiplets showing their description via these Adinkras.

Conjecture that all off-shell 4D, N=1 supermultiplets are characterized by two integers corresponding to these Adinkras.

Abstract

Presented in this paper the nature of the supersymmetrical representation theory behind 4D, N = 1 theories, as described by component fields, is investigated using the tools of Adinkras and Garden Algebras. A survey of familiar matter multiplets using these techniques reveals they are described by two fundamental valise Adinkras that are given the names of the cis-Valise (c-V) and the trans-Valise (t-V). A conjecture is made that all off-shell 4D, N = 1 component descriptions of supermultiplets are associated with two integers - the numbers of c-V and t-V Adinkras that occur in the representation.