Structural Theory of 2-d Adinkras

TL;DR

This paper classifies all 2-dimensional Adinkras, a combinatorial tool for supersymmetry representations, confirming a key conjecture and providing new structural insights into their underlying codes.

Contribution

It provides a complete classification of 2-d Adinkras and characterizes the associated even-split doubly even codes, advancing the understanding of supersymmetry representations.

Findings

Confirmed H"ubsch's conjecture on 2-d Adinkras.

Provided a simple characterization of even-split doubly even codes.

Classified all 2-d Adinkras comprehensively.

Abstract

Adinkras are combinatorial objects developed to study 1-dimensional supersymmetry representations. Recently, 2-d Adinkras have been developed to study 2-dimensional supersymmetry. In this paper, we classify all 2-d Adinkras, confirming a conjecture of T. H\"ubsch. Along the way, we obtain other structural results, including a simple characterization of H\"ubsch's even-split doubly even code.