Structural Theory and Classification of 2D Adinkras

Abstract

Adinkras are combinatorial objects developed to study (1-dimensional) supersymmetry representations. Recently, 2D Adinkras have been developed to study 2-dimensional supersymmetry. In this paper, we classify all 2D Adinkras, confirming a conjecture of T. Hübsch. Along the way, we obtain other structural results, including a simple characterization of Hübsch’s even-split doubly even codes.